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Spatial and temporal variability of double diffusive structures in Powell Lake, British Columbia Zaloga, Artem 2015

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Spatial and Temporal Variability of Double Diffusive Structuresin Powell Lake, British ColumbiabyArtem ZalogaB. Sc. Engineering Physics, Queen’s University, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Oceanography)The University of British Columbia(Vancouver)December 2015c© Artem Zaloga, 2015AbstractThe spatial and temporal properties of naturally occurring double diffusive (DD) structures presentin the bottom waters of Powell Lake, British Columbia were investigated. Observations were ob-tained from four annual surveys consisting of vertical cm-resolution conductivity-temperature-depth(CTD) profiles along the 9 km length of the lake, and from a month-long mooring consisting ofthirty-eight temperature sensors and two current meters.DD layers were identified by isolating clusters on temperature-salinity (T-S) diagrams, andtracked spatially and temporally throughout each of the CTD surveys. The layers were observedto be persistent over four years, and horizontally coherent over the entire lake length at depths of336-347 m. In this region the vertical density ratio (a non-dimensional measure of the relativestrengths of vertical temperature and salinity gradients), Rρz, and buoyancy frequency, N, were nearconstant at Rρz = 2.2± 0.2 and N = (2.3± 0.3)× 10−3 s−1, and the Rayleigh number reached apeak at Ra≈ 107. Layers just above and below this region were less horizontally-coherent and withlarger values of Rρz and N.Spatial variations in layer depth and the background temperature/salinity distribution showedpersistent trends throughout the study period. These trends indicated that layer slope and horizontalproperty gradients are linked and that the horizontal density ratio may be an indicator of the meanlayer slope. Linear fits to the layer properties indicated that a horizontal density ratio of Rρx =−0.35±0.17 was accompanied by a mean layer slope of ∆z/∆x= 0.05±0.02 m/km.An individual DD step within one of the stable and horizontally coherent DD layers was iden-tified within the moored temperature time series and tracked over the course of a week. The con-vective regime within the DD step was observed to be composed of intermittent thermal plumesemitted from the bottom diffusive interface. The features appeared as a common peak in the meanDD step temperature and horizontal velocity power spectra. The plumes had a period of ∼ 22 min-utes (coinciding well with the buoyancy period within the diffusive interface), a temperature scaleof T ′ ≈ 0.2 m◦C, and horizontal and vertical velocity scales of u′ = w′ ≈ 0.5 mm/s.iiPrefaceThis thesis is original and unpublished work carried out by the author, Artem Zaloga, under thesupervision of Richard Pawlowicz. CTD surveys during the years of 2012 and 2013 were conductedby Benjamin Scheifele and Richard Pawlowicz, and during the years of 2014 and 2015 by the author,alone and with Richard Pawlowicz. The mooring was designed and built by the author with theassistance of Roger Pieters and Steve Pond. All field work was conducted with the assistance of thesea-going technicians, Chris Payne and Larysa Pakhomova. Figure 2.1 and Figure 4.2 are adaptedwith permission from Scheifele et al. (2014) and Turner and Chen (1974) respectively.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii1 Introduction and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 The Double Diffusive Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Laboratory Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Field Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Numerical Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Research Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Research Site and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 Powell Lake, British Columbia . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Annual CTD Profiling Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Temperature Sensor and Current Meter Mooring . . . . . . . . . . . . . . . . . . . 163 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Structure and Dynamics of DD Layers . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Motions Within the Lake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 Dynamics Within a DD Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Discussion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.1 Convective Regime Within DD Layers . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Horizontal Coherence of DD Layers . . . . . . . . . . . . . . . . . . . . . . . . . 404.3 Variability of DD Layer Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4 Summary and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49ivList of FiguresFigure 1.1 Schematic of Double Diffusive Convection Structure . . . . . . . . . . . . . . 2Figure 1.2 Schematic of the Density Flux Ratio Regimes . . . . . . . . . . . . . . . . . . 4Figure 2.1 Powell Lake Location; Adapted from Scheifele et al. (2014) . . . . . . . . . . 12Figure 2.2 Temperature and Salinity Structure in Powell Lake . . . . . . . . . . . . . . . 13Figure 2.3 Sampling Locations in Powell Lake . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.4 Powell Lake Level Heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.5 Schematic of the Temperature Sensor-Current Meter Mooring . . . . . . . . . 17Figure 2.6 Moored Currents Record . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 3.1 Identification of DD Steps Within CTD Data . . . . . . . . . . . . . . . . . . 22Figure 3.2 Layer Clusters on T-S Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 3.3 Vertical Structure of the DD Layers . . . . . . . . . . . . . . . . . . . . . . . 24Figure 3.4 Rρz, N, and Ra of the DD Layers . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.5 Salinity, Temperature, and Density Structure of the DD Layers . . . . . . . . . 26Figure 3.6 Mean DD Layer Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 3.7 Wind, Air Pressure, and Lake Currents . . . . . . . . . . . . . . . . . . . . . . 28Figure 3.8 Moored Temperature Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . 29Figure 3.9 Vertical and Horizontal Lake Motions . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.10 Moored Temperature and Current Records . . . . . . . . . . . . . . . . . . . . 31Figure 3.11 DD Step Appearance in the Temperature Record . . . . . . . . . . . . . . . . 32Figure 3.12 Identification and Tracking of a Single DD Step . . . . . . . . . . . . . . . . . 33Figure 3.13 Power Spectra of DD Step Properties . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.14 Band-Passed Temperature and Horizontal Displacement Records . . . . . . . . 35Figure 3.15 Intermittent Buoyant Plumes Within DD Step . . . . . . . . . . . . . . . . . . 36Figure 4.1 Layers with Background Temperature Field . . . . . . . . . . . . . . . . . . . 43Figure 4.2 Circulation Within Tilted DD layers; Adapted from Turner and Chen (1974). . 44vAcknowledgmentsI would like to thankStephanie Waterman, Gregory Lawrence, and Susan Allen for taking the time to edit this work;Roger Pieters and Steven Pond for the immense amount of assistance with all of the instruments;Chris Payne and Larysa Pakhomova for the tireless hours spent sampling on that damn lake.I would also like to specifically thank my supervisor, Richard Pawlowicz, for the countless hoursspent helping me throughout this work and, in effect, stretching the boundaries of my mind.And I would like to thank my dear friends and family for ensuring that those boundaries didn’tdrift into insanity... too often. How you put up with me, I’ve no idea.viDedicationTo Charlie.viiChapter 1Introduction and BackgroundIn an oceanographic setting, the dynamically important aspects of the density of water are primarilydetermined by the salt content and temperature of the water. In the case where the overall verticaldensity gradient is gravitationally stable but either one of temperature or salinity have an unstablevertical gradient, the very different molecular diffusivities of heat and salt can give rise to a class ofinstabilities known as double diffusive instabilities.Via molecular diffusion, these instabilities transfer the potential energy stored in the unstablegradient into convective motions within the water column; convective motions which themselveshave a tendency to organize into large scale structures within the ocean and many lakes. Thesestructures can cover large horizontal areas, and although their importance for the global ocean cir-culation is uncertain (Ruddick and Gargett, 2003), their existence is observed in many parts of theocean, especially in the Arctic. The purpose of this work is to further investigate the spatial andtemporal properties of these structures in a natural environment, in order to compare with previouslaboratory and numerical studies, as well as to better predict their effects on the vertical transport ofheat and salt within the ocean.1.1 The Double Diffusive InstabilityEven if the overall density gradient of a water mass is gravitationally stable (increasing mono-tonically with depth) it may still be susceptible to convective instabilities if either the salinity ortemperature gradients of the water mass are unstably stratified. This is due to the fact that themolecular diffusivity of heat is greater than that of salt by a factor of about 100, which results intemperature gradients evolving at a more rapid rate than those of salt. Under certain circumstancesthis may create regions with small buoyant instabilities, so that the potential energy stored up inthe destabilizing gradient is partially converted into convective motions via these instabilities. Thisphenomenon was first proposed theoretically by Stern (1960), and is now described by the termdouble diffusive convection.There are two possible arrangements of salinity and temperature gradients (with one stabilizingand the other destabilizing the system) that create a stable density profile – resulting in two different1Temperature Salinity Depth Figure 1.1: Left to right: An example of the characteristic staircase structure observed invertical profiles of temperature (blue) and salinity (red) within the diffusive layeringregime; the associated schematic depicting the convective regions (dark grey eddies) anddiffusive interfaces (empty grey).instability modes. The first occurs when both gradients decrease monotonically with depth, produc-ing a stabilizing temperature gradient and destabilizing salinity gradient; the second occurs whenboth gradients increase with depth, producing temperature and salinity gradients with the converseeffects. The former mode is called ‘Salt Fingering’ due to the propensity of the instabilities to de-velop as vertical, finger-like protrusions; the latter mode is called ‘Diffusive Layering’ due to theobservation of these instabilities primarily after they have evolved into a layered structure.In the ocean, the salt fingering mode is dominant in mid-latitudes (Kunze, 2003) where warm,salty waters overlie colder, fresher waters, whereas the diffusive layering mode is dominant in high-latitude regions (Kelley et al., 2003) where cold, fresh waters overlie warmer, saltier waters. In bothcases, the instabilities can be identified because of a common feature observed in both modes: theyhave a tendency to evolve into stacks of horizontal layers which are observed as staircase structuresin vertical temperature and salinity profiles (Figure 1.1, left). These layers are composed of watermasses with differing, but still gravitationally stable, densities, and the resulting staircase structureis considered an indicator of double diffusive instabilities.Schematically, these layers are understood to consist of ‘convective regions’ (‘risers’ in the stair-cases) with near uniform properties, sandwiched vertically between ‘diffusive interfaces’ (‘treads’in the staircases) with high gradients of both temperature and salinity (Figure 1.1, right). As theterms imply, fluxes in the convective regions are governed by active convection, and fluxes throughthe diffusive interfaces are thought to be governed by molecular diffusion only.The present work is concerned solely with the diffusive layering mode of the instability, but theinterested reader is referred to the reviews by Kunze (2003) and Radko (2013) for further readinginto the salt fingering mode of the instability.21.2 Laboratory ObservationsThe original stability analysis of linear gradients of temperature and salinity presented by Stern(1960) focused mainly on the salt fingering mode and left the diffusive layering mode to a merefootnote. However, due to the symmetry of the equations for the two modes (one needs only tochange the signs on the assumed temperature and salinity gradients to go from one mode to theother), the main conclusion equally applies to the diffusive mode as well: that a seemingly stablestratification may actually be unstable.This revelation spurred laboratory experiments dealing with the heating of salt stratified fluidsand similar sugar-salt1 systems. Based on these experiments and dimensional arguments, it wassuggested that the properties of the staircases formed would depend only on differences betweenthe properties of the convective regions – specifically the ratio of neighbouring temperature andsalinity differences, ∆T and ∆S, between these convective regions (Turner, 1965). This implies thatone of the main non-dimensional governing parameters for this system should be the density ratio,which for the diffusive mode is defined asRρ ≡ β∆Sα∆T (1.1)where α (≡− 1ρ0∂ρ∂T ) and β (≡ 1ρ0∂ρ∂S ) are the thermal expansion and haline contraction coefficientsassuming some reference density, ρ0. This ratio can be interpreted as a comparison between thestabilizing effects of the salinity differences and destabilizing effects of the temperature differencesbetween steps on the the overall stratification, such that the system is more stable for high values ofRρ and convectively unstable for Rρ 6 1.Aside from the density ratio, the other non-dimensional numbers that are thought to govern thissystem include: the Prandtl number, Pr ≡ ν/kT , where ν is the kinematic viscosity and kT is thethermal diffusivity; the salinity Lewis number, τ ≡ kT/kS, where kS is the diffusivity of salt; and(once staircases form with convection within the layers) the Rayleigh number,Ra≡ ( gαkTν)∆TH3 (1.2)where H is the layer thickness/height and g is the acceleration due to gravity.Laboratory experiments have shown that in a stable salt-stratified system, heating from the bot-tom results in the formation of a (time-dependent) bottom convecting layer, followed by the forma-tion of more layers above over time (Turner, 1968). This occurs because the buoyancy instabilitiesgenerated by the heating of the bottom are constrained to a maximum height by the stabilizing ef-fects of the salinity gradient, and so create the first convective layer. Just above this convective layer,a high gradient region is created where the only transport processes are due to molecular diffusion1Due to the difficulty of perfectly isolating heat diffusion though side walls in physical experiments, the salt-heatsystem is at times replaced by the sugar-salt system. The replacement is not perfect, since the diffusivities of the sugar-salt system differ by a factor of 3 while those of the salt-heat system differ by a factor of 100, but still serves to exemplifythe characteristics of double diffusive processes.3Convectively Unstable  No DD layers  Overturning convection 𝜸 =𝜷𝑭𝑺𝜶𝑭𝑻  𝑹𝝆 =𝜷𝜟𝑺𝜶𝜟𝑻  0.15 1 2 ~7 10 γ-instability  DD layers unstable/ merging  3D turbulent convection  1 DD Structures present γ roughly constant  DD Layers stable  Intermittent thermal plumes γ increases  DD interfaces get thicker  Convection gets weaker Ra Important Figure 1.2: A schematic of the functional form of the density flux ratio, γ , as a function of thedensity ratio, Rρ , with the characteristics of each regime shown.– this is the diffusive interface. Since heat diffuses quicker than salt, buoyancy instabilities are gen-erated at the upper boundary of this diffusive interface, and so begin the development of the nextconvective layer.Interest in the transport properties through the diffusive interface led to more laboratory studiesfocusing specifically on a two layer system with a diffusive interface, heated from below and, attimes, cooled from above. It was shown that the interface has a thickness that depends on Rρ ,and has a tendency to migrate vertically, with the migration rate increasing as Rρ approaches 1from higher values (Marmorino and Caldwell, 1976). It was also found that the transport in theconvective regions is dominated by mechanical mixing for 1 < Rρ 6 2, and by interface-dependentdouble diffusive convection for Rρ > 2 (Crapper, 1975).Since the heating in these experiments could be controlled, the total vertical heat flux2, FT (inunits of ◦C×m/s), through the interface was determined and found to decrease with increasing Rρ(Turner, 1965). An important parameter that appears in this analysis is the density flux ratio, definedasγ ≡ βFSαFT(1.3)where FS is the salt flux (in units of g/kg×m/s), and indicates the ratio between the (non-dimensional)stabilizing flux due to salinity and the destabilizing flux due to temperature. Alternatively, the den-sity flux ratio can be interpreted to indicate the contribution of the potential energy released from thetemperature field which goes into moving the salt. It was shown by Turner (1965) that the densityflux ratio is nearly constant at γ ≈ 0.15 for 26 Rρ < 7, and increases towards a value of 1 when Rρapproaches 1 from higher values (Figure 1.2). This was extended by Newell (1984), who showed2The parametrization of double diffusive fluxes has been an active ongoing endeavor, but as the present work does notrely on such parameterizations the reader is referred to Kelley et al. (2003) for a historic perspective on their development.4that γ ≈ 0.15 up until Rρ ≈ 10, after which it begins to increase again. As Rρ increases above thisvalue, γ tends towards kSkT Rρ for a diffusion-governed background since the fluxes would dependonly on the molecular diffusivities (Newell, 1984), or towards Rρ for a background dominated byturbulence since the fluxes would be dominated by eddy diffusivity (Radko, 2013). In this high Rρlimit, erosion of the diffusive interface becomes significant – that is, the thickness of the diffusiveinterface increases while the slope of the gradient decreases.During observations of two dimensional effects on layer formation in sugar-salt experiments,it was found that sloped walls and local sources of anomalies set up horizontal gradients, whichled to horizontal layer formation (Turner and Chen, 1974). The layers propagated from the slopedwalls/anomaly sources until they filled the domain, and then proceeded to merge until they becamestable and the merging process ended. Once stabilized, the layers were found to tilt slightly, with alarge-scale circulation occurring along the top and bottom diffusive interfaces. The horizontal fluxesof temperature and salinity within the layers were observed to be slightly unbalanced, resulting in ahorizontal density gradient along the tilted layers.After the initial laboratory experiments during the birth of the field, focus shifted to numericalsimulations and field observations. Much later work on the laboratory salt-heat system by Laveryand Ross (2007) showed that the diffusive interfaces were subjected to interface waves, with thermalplumes observed emerging from them. Furthermore, Lavery and Ross (2007) showed that the inter-faces had a tendency to get thicker for increasing Rρ , supporting the earlier results of Marmorinoand Caldwell (1976). A later study by Ross and Lavery (2009) using acoustic measurements of thesalt-heat system indicated that layer migration and merger were prominent, and that convection isdriven by the thermal plumes (which are dependent upon the applied heat flux) released from thediffusive interface.Turner (1968), Marmorino and Caldwell (1976), and Newell (1984) all observed oscillationsin the temperature records near the diffusive interface, with the amplitude of the temperature os-cillations decreasing with increasing Rρ (Newell, 1984). Turner (1968) observed these oscillationswith a period on the order of 10 times the background buoyancy period, 2pi/N, where the buoyancyfrequency, N, is defined asN ≡√−gρ0dρdz=√g(αdT/dz−βdS/dz) (1.4)whereas Marmorino and Caldwell (1976) observed these oscillations with a period on the order ofthe interface buoyancy frequency, 2pi/NI , where NI has the same form as N but is calculated withinthe diffusive interface only.These oscillations were interpreted to be the same plume features observed later by Lavery andRoss (2007) and Ross and Lavery (2009). Turner (1968) specifically noted that the oscillationswere intermittent and occurred prior to the system transitioning into the convective mode during thedevelopment of the second convective layer.51.3 Field ObservationsThe layer-based definition for the density ratio Rρ (Equation 1.1) is better suited for laboratorystudies rather than for field observations due to the explicit use of the temperature and salinitydifferences between layers. Instead, for field observations, the definition ofRρz ≡ β∂S/∂ zα∂T/∂ z (1.5)is more convenient. This definition is equivalent to Equation 1.1 if the temperature and salinityprofiles are first smoothed over the steps prior to any calculation of gradients, which is the standardapproach. In this context, Rρz can be interpreted as the ratio between the stabilizing effects of thebackground salinity gradient and destabilizing effects of the background temperature gradient onthe overall stratification. It is typically in the range of 1− 10 in field observations where doublediffusive processes occur.One of the earliest field observations of double diffusive structures was performed by Hoare(1968) in Lake Vanda, Antarctic. Several double diffusive layers were observed to exist over thecourse of nearly a year. The layers spanned a horizontal distance of 4 km, and showed temporalvariability in their temperatures, thicknesses, and depths.Afterwards, many observations of double diffusive staircases came from the Arctic Ocean: Pad-man and Dillon (1987), Timmermans et al. (2008), Zhou and Lu (2013), Zhou et al. (2014), andCarmack et al. (2012) observed the structures in the Canada Basin; Sirevaag and Fer (2012) in theAmundsen Basin; and Polyakov et al. (2012) in the Laptev Sea. Data were typically obtained bymeans of (ship-based or moored) conductivity-temperature-depth (CTD) profilers or microstructureprofilers.Within the Canada Basin, the staircase structures were observed to be persistent over twodecades (Carmack et al., 2012) and horizontally coherent over 800 km, breaking only at the bound-aries (Timmermans et al., 2008). It was shown that the bottom-most convective layer was caused bygeothermal forcing (Zhou et al., 2014), and that the entire structure acts as a thermal barrier to thisforcing (Zhou and Lu, 2013). Interestingly, no horizontal coherence was observed in layers seen inthe neighbouring Amundsen Basin (Sirevaag and Fer, 2012).The steps within the Arctic staircase structure were found to be non-uniform in height, possiblyimplying non-uniform fluxes through the staircase structure (Padman and Dillon, 1987). It wasfurther suggested that the convective structure within layers changed from intermittent buoyantplumes to convection cells as Rρz approaches 1 from higher values (Padman and Dillon, 1987),similar to those seen in the buoyant convection of single component fluids. These suggestionswere supported by the observation that the steps are in a mild state of turbulence, with signals ofintermittent small-scale flow structures within the convective regions of the steps, impinging uponthe diffusive interfaces (Zhou and Lu, 2013).In the Laptev Sea, Polyakov et al. (2012) observed that the staircase structure was also visiblein vertical profiles of horizontal currents, and that the shear produced by these structures was not6enough to overcome the effects of buoyancy in the diffusive interfaces. Furthermore, it was shownthat the layers were getting warmer, saltier, and lighter with time, and that their properties wereunaffected by passing eddies.Apart from the Arctic and Antarctic regions, double diffusive structures have also been observedin several lakes around the world. The most prominent and persistent examples include: Lake Nyosin Cameroon (Schmid et al., 2004), Lake Kivu on the border of Rwanda and the Democratic Repub-lic of Congo (Schmid et al., 2010; Sommer et al., 2013), and Powell Lake in Canada (Scheifele et al.,2014). The structures are also seen more intermittently in other lakes, appearing and disappearingwith changes in the seasonal stratification (von Rohden et al., 2010).Within these lakes, it was observed that the structures develop from and are maintained byexternal sources such as large surface cooling events (Schmid et al., 2004) or geothermal bottomheating (Scheifele et al., 2014). In the former case, it was observed that the staircase structureformed over the period of 9 months after the cooling event; in the latter, staircase formation maybe the result of hundreds or thousands of years of weak heating. The layers were observed to behorizontally coherent for scales on the order of many kilometers (Schmid et al., 2010; Scheifeleet al., 2014), but may be disturbed by horizontal intrusions (Schmid et al., 2010).A closer inspection of the diffusive steps revealed that the temperature interfaces were thickerthan salinity interfaces (Sommer et al., 2013), and that the layers are in a state of active convection(Schmid et al., 2010). It was further observed by Scheifele et al. (2014) that for Rρz . 3 the systembegan to exhibit a dependence on the Rayleigh number, which is indicative of a regime similar tothat of single component buoyant convection. These observations reinforce the idea of intermittentbuoyancy driven convective instabilities arising from the diffusive interface, with a transition toturbulent convection for low density ratios.1.4 Numerical ModellingAt the same time that double diffusive convection was being studied in laboratory and field settings,numerous analytic expressions and numerical models were developed to investigate the behaviourof the diffusive interface and resulting staircase structure. A one-dimensional numerical modelwas created by Shirtcliffe (1969) in order to simulate a stable salt-stratified gradient heated frombelow. In the model, the molecular diffusivity was replaced by an eddy diffusivity in buoyantlyunstable regions to mimic the effects of convective eddies. This model successfully reproducedthe formation and evolution of the bottom convecting layer – as well as the development of thefollowing layers – from initially linear gradients, and suggested that the schematic of convectingregions separated by diffusive interfaces was a correct interpretation of the staircase structure. Asimilar one-dimensional model was described more recently by Toffolon et al. (2015), and (withtuning) was used to reproduce the staircase structure in Lake Kivi, Lake Nyos, and Powell Lake.Linear stability analysis and direct numerical simulation (DNS) of the development of doublediffusive instabilities from initially linear gradients by Noguchi and Niino (2010a) showed that theinstabilities begin as exponentially growing vertical oscillations, consistent with linear theory, and7develop into overturning convection. After attaining some critical Rρ , the instability field sponta-neously develops into layers which grow slowly in thickness, and merge over time. Noguchi andNiino (2010b) further showed that the layer mergers occur in two forms: one where the diffusiveinterface erodes, and the second where a convective layer erodes. These mergers were shown to bethe result of vertically asymmetric turbulent entrainment from adjacent layers.Although examined primarily with interest in the astrophysical case3, Rosenblum et al. (2011)showed again that the initial exponential growth of instabilities is consistent with linear theory.Furthermore, they also showed that the formation of the staircase structure is consistent with aproposed mechanism responsible for layer formation in the salt finger mode – the γ instability(Radko, 2003).In a linear stability analysis of perturbations to a linear gradient system by Radko (2003), itwas found that the growth rate eigenvalues of the characteristic equation have a positive real root– implying exponential growth – only when γ is a decreasing function of Rρ . This γ instabilityimplies that vertical differences in γ will grow in this regime, and result in vertical convergencesand divergences of salt and heat, which lead to the formation of layers. As this only occurs in theregion for which γ is a decreasing function of Rρ , for the diffusive mode this would imply that layergrowth (and merging) is only possible for Rρ < 2.The stability of an established diffusive interface was studied by Huppert (1971), who showedthat the interfaces within the staircase structure were unstable for Rρ < 2, resulting in layers mergingconsistently until reaching a stable state. It was noted that this was a local criterion only, and thatmerging may continue in other regions even if one section is stable.A study performed by Linden and Shirtcliffe (1978) of the double boundary (one for temper-ature, one for salinity) structure of an individual diffusive interface showed that the convection isintermittent and reminiscent of the convective instabilities that occur in the fingering mode (Stern,1969). Their model of the interface worked best for 36 Rρ 6 7; at larger Rρ the convection was tooweak to remove the buildup of temperature and salinity at the interface, whereas below this rangeinterface entrainment from the convective regions became important and increased the fluxes. Itwas later shown by Flanagan et al. (2013) that 3D effects (which are an indicator of turbulent con-vection) only become prominent for Rρ 6 2. This reinforces the idea that convection gets strongerin the layers as Rρ approaches 1, from higher values.Further work by Carpenter et al. (2012) on the linear stability and direct numerical simulation(DNS) of a single diffusive interface indicated that the instabilities develop in the boundary layersof the interface, as opposed to within the interface core. Furthermore, the instabilities were foundto be of the purely convective type, and are therefore time-dependent.3Although presented here as an oceanographic phenomenon, double diffusive convection is found in many otherfields where compositional gradients that oppose one another are found. Some examples include structure and evolutionof stars and planets in an astrophysical context (e.g. Nettelmann et al. (2015)) and multi component alloy solidificationin metallurgy (e.g.Beckermann and Viskanta (1989)).81.5 Research FocusTo date, the work done in the field, laboratory, and numerical studies of the diffusive layeringmode of double diffusive convection is consistent with the common explanation for the mechanismsinvolved in the process. The use of the density ratio, Rρ , as the main governing parameter hasbecome standard, along with the 1 < Rρ < 10 range for the identification of where double diffusiveprocesses can occur (Figure 1.2).Spontaneously emerging staircase structures are ubiquitous, and used as a main identifier for theoccurrence of double diffusive convection. The explanation that the staircase structure is a productof vertically stacked convective layers inter-spaced by molecular-diffusion governed interfaces isstrongly supported. Layers have been observed to form and merge, and thus be unstable, for Rρ 6 2,but stable for Rρ > 2. Layer merging is most likely explained by differences in the convectiveentrainment between adjacent layers.The formation mechanism of these structures is still contested, but likely caused by verticaldeviations in the amount of energy transfered from the destabilizing temperature gradient into theconvective motions, which rearrange the stabilizing salinity gradient. This energy transfer is encom-passed in the density flux ratio, γ . It is observed that γ is a decreasing function of Rρ for Rρ 6 2, isnear constant for 2 < Rρ 6 10, and an increasing function of Rρ for Rρ > 10.Numerical studies have indicated that as Rρ approaches 1 (from higher values) the convectiveregime within the layers changes from intermittent buoyant plumes to fully three-dimensional tur-bulent convection, where the governing parameter switches from Rρ to Ra; the transition regionbetween the two regimes occurs at Rρ ≈ 2. The plumes are formed in the thermal boundary layer ofthe interface and so depend on its existence.An important aspect of this field of study is the proper modelling of the transport propertiesthrough these double-diffusive structures, and although much work has been done in studying themechanisms involved in double diffusive convection, a more complete understanding of the physicalprocesses involved is still desired. In this respect, the numerical and laboratory studies of doublediffusive convection are far more advanced than observational studies, and much work needs to bedone to bring the observational results to the level of the other two approaches.This lag in field observations exists primarily because of restrictions in sampling procedures,such that vertical temperature and salinity profiles are attained either at multiple locations aroundthe same time, or at one location over time. In both cases only two dimensions of the staircasestructure and evolution are covered. Furthermore, due to the inherent noise in natural environments,it has been difficult to precisely detect what is occurring within the layered structure in these envi-ronments.Due to this need for reconciliation between field studies and numerical/laboratory studies, theaim of the present work is to further observe and describe both the spatial structure and temporalevolution of the double diffusive staircase structure in a natural environment. The main goal is tocharacterize the dynamics of both the overall staircase structure, as well as the features within theindividual layers that make up that structure.9The dynamics of the entire staircase structure should help elucidate possible formation andmaintenance mechanisms of these large scale structures, which can then be compared to the mech-anisms for staircase formation proposed by laboratory and numerical studies. Any variability ofthe structure of the layers could help identify possible factors which contribute to the large scaleproperties of these structures. Comparison of the observed variability of the layers with the layersobtained from numerical studies would help validate the assumptions behind those studies, specif-ically whether or not a one dimensional approach is appropriate in modelling the double diffusivesystem.Study of the variability within the layers could help identify the convective regime within thelayers, which is imperative to properly understanding and modelling the fluxes through these struc-tures. A more complete understanding of the convective regime within the layers would ultimatelyassist in creating better parameterizations of the fluxes through double diffusive structures, whichcould be used to better model the transport of heat and salt throughout the ocean.10Chapter 2Research Site and MethodsThe intention of this work is to describe the spatial and temporal properties of double diffusive(DD) staircase structures in the diffusive regime, as seen in the relatively stable environment ofPowell Lake, British Columbia. To properly describe the dynamics of these structures, observationswere made of the structure and temporal evolution of both the individual steps, on the scales ofcentimetres and minutes, as well as the entire staircase structure, on the scales of kilometres andyears.The structure and dynamics of the overall staircase structure were studied using a data set ob-tained from four annual research trips, consisting of centimetre-scale (in the vertical) conductivity-temperature-depth (CTD) profiles at various locations along the length of the south basin of the lake.The dynamics of an individual step within this structure were studied using a data set obtained froma month-long mooring deployment consisting of thirty eight temperature probes and two currentmeters.2.1 Powell Lake, British ColumbiaPowell Lake is located near the city of Powell River, BC, approximately 170 km north-west ofVancouver along the Sunshine Coast (Figure 2.1). It is a meromictic lake that was once a fjordconnected to the Strait of Georgia. However, roughly 11,000 years ago, it was landlocked due topost-glacial isostatic rebound after the last ice age. After this event, its southern sill rose, and hencethe lake surface is now roughly 50 m above sea level (Mathews et al., 1970).The lake is roughly 50 km long and 2 km wide, with six basins connected by shallower sills,first observed in a bathymetry study conducted by Mathews (1962). The lake has steep sides with aflat bottom – common to ex-fjords – and reaches a maximum depth of around 350 m in the southernbasin. Williams et al. (1961) found that the two southernmost basins contain warmer, trapped relicsea water, which is transported vertically primarily by molecular diffusion (Sanderson et al., 1986).The other four, northern basins are relatively fresh. This is likely because most of the fresh waterinput is into those basins, where turbidity currents can flush the basin floors during sedimentarydischarge (Sanderson et al., 1986).11 36’  32’  124oW  28.00’  24’  20’  55’   50oN   5’  10’  15’ 0510 kmStrait of GeorgiaSouth Basin - with relic seawaterEast Basin - with relic seawaterSill at 290 mSill at25 mSill at12 mFour northern basins contain no relic seawaterPowell River:primary freshwater input(b) 126oW  125oW  124oW  123oW   48oN  30’   49oN  30’   50oN  30’   51oN  30’ 50 kmPowell LakeVancouverVancouverIslandStrait of Georgia(a)Figure 2.1: a) The location of Powell Lake, in Powell River, BC. b) The six flat-bottomedbasins of Powell Lake are shaded in dark grey; the South Basin being the location ofstudy. Adapted from Scheifele et al. (2014). c©American Meteorological Society. Usedwith permission.The lake bottom of the southern-most basin is composed of a methane and pyrite rich “gelatinousooze” (Sanderson et al., 1986), with the trapped relic sea water near the bottom containing highlevels of hydrogen sulphide, pyrite, and iron sulphide (Perry and Pedersen, 1993). The near-surfacefreshwater exits into the Strait of Georgia via a man-made dam on the south side of the southernbasin, which raised the lake level by a few metres when it was completed in 1912.The presence of warm salty water near the bottom suggests a high susceptibility to doublediffusive instabilities. A micro-structure study performed by Osborn (1973) showed irregular tem-perature gradient variations near the lake bottom. By means of analyzing sediment core samples,Hyndman (1976) found that the geothermal heat flux was 27 ± 11 mW/m2 at the lake bottom.A more recent study dealing specifically with the DD properties of the lake was conducted byScheifele et al. (2014). Their study showed that there were several vertical regions below 250 m,where staircases indicating DD instability could be found (Figure 2.2a). Their work focused oncharacterizing the statistical properties of the DD steps found in the relic salt water region below adepth of 325 m, which exhibited the most coherent DD structures.The DD steps were found to have a mean mixed layer height of 70 cm, a mean diffusive inter-127 7.5 8 8.5 9 9.5250260270280290300310320330340In−Situ Temperature [ oC]4 6 8 10 12 14 16Reference Salinity [g/kg]Depth [m](a)9.301 9.302 9.303 9.304 9.305 9.306 9.307 9.308332.6332.8333333.2333.4333.6333.8334In−Situ Temperature [ oC]16.678 16.6785 16.679 16.6795 16.68 16.6805Reference Salinity [g/kg]Depth [m](b)Figure 2.2: a) In-situ temperature and Reference Salinity profiles of the salt water layer in thesouthern basin of Powell Lake. DD active regions are shaded in gray. b) Close-up of afew DD steps in the lowest DD active region, near the lake bottom; raw data shown inthin lines and smoothed profiles in which electronic noise is filtered out in bold.face height of 20 cm, and mean differences between steps of 4 m◦C in temperature and 2 mg/kg insalinity1. Furthermore, consistent estimates of the heat flux though interfaces in the staircase struc-ture and in the linear temperature gradient region at 320 m were found to be in agreement with thevalue previously found by Hyndman (1976) in the bottom sediments. Following the observations ofScheifele et al. (2014), the focus of the present work is again only on this lowest DD active region,below a depth of 325 m.2.2 Annual CTD Profiling SurveysBeginning in 2012, an annual survey using a CTD profiler was carried out in order to observe thedynamics of the overall staircase structure in the southern basin of Powell Lake. The survey in-volved taking a number of vertical CTD profiles along the length of the lake2 during each samplingtrip (Figure 2.3). The CTD data obtained over the four years included: 21 profiles from July 2012,capturing the middle and northern sections of the lake; 18 profiles from June 2013, capturing thesouthern and central sections; 11 profiles from May 2014, capturing the southern and central sec-tions; and 7 profiles from June 2015, capturing the entire lake but at a larger profile spacing.Of the 57 CTD profiles obtained in the four annual surveys, only 49 were used in the identifica-tion of the DD steps and layers3. This was because 4 profiles from the 2013 survey, 2 profiles fromthe 2014 survey, and 2 profiles from the 2015 survey reached bottom before entering the bottom DD1All salinity values stated are on the TEOS-10 Reference-Composition Salinity Scale with no salinity anomaly (IOCet al., 2010).2The term ‘lake’ will be implied to refer to the southern basin of Powell Lake only.3Any further use of the terms ‘steps’ and ‘layers’ will be understood to refer to DD steps and DD layers.13active region. These profiles were in the southern part of the lake.The CTD profiler used for these surveys was a Sea Bird SBE 254, which was set to its maximumsampling rate of 8 s−1. In order to resolve the length scales of the DD steps (typically less than 1m), the lowering rate of the profiler was chosen to be 10 cm/s in the salt water region (depths below250 m) and 1 m/s above this region. This procedure was arranged in order to save time, but even so,each cast took around 45 minutes to complete. The combination of the 8 s−1 sampling rate and 10cm/s drop rate resulted in a vertical resolution of ∼1.5 cm.The response time of the CTD temperature sensor is 0.1 s, whereas the conductivity sensor’stime response is best described by the quotient of the sensor volume and the pump flow rate: 2.4mL ÷ 15 mL/s ≈ 0.16 s (Scheifele, 2013). At a lowering rate of 10 cm/s, these responses produce aspatial resolution of 1 cm and 1.6 cm in the temperature and salinity time series, respectively. Theseresolutions correspond to the smoothing effects that the sensors produce in response to instantaneouschanges in temperature and salinity; they were not corrected for in subsequent processing since theywere of the same order as the resolution due to the lowering rate and sampling frequency. The twosensors were connected in series, so that the conductivity sensor would sample a parcel of water0.2 s later than the temperature sensor. This temporal offset between sensors was corrected for byapplying a 0.2 s time shift to the conductivity data during preprocessing.The temperature and salinity resolutions of the time series were 0.1 m◦C and 0.1 mg/kg, and theelectronic noise in the signals was estimated to be ± 0.2 m◦C and ± 0.1 mg/kg, respectively. Thisnoise can be seen as the variability in the raw data of Figure 2.2b in the region between 333.4 m and333.8 m.The manufacturer’s quote for the temperature sensor’s maximum calibration drift rate is 2m◦C/yr, but no deviations were evident in the data or independent calibrations and thus no cor-rections were made over the 4 year series. Conductivity measurements did change from year toyear, and intermittent calibrations were not accurate enough to fully remove these drifts. Instead,the data were manually adjusted so that waters of the same temperature had the same salinity; the2013 survey salinity data was adjusted by +8.4mg/kg, the 2014 data by +5.5mg/kg, and the 2015data by +22.1mg/kg.Since the CTD profiler was connected to the boat winch via a cable, any boat motions weretransferred to the movement of the CTD profiler, which could introduce variability into the temper-ature and salinity data. This variability would appear similar to the noise in the sensors but would bemore intermittent. In order to minimize this movement-related noise the sampling was performedbetween sunset and sunrise, when the wind and waves were most calm. A ‘lander’ cage was at-tached to the CTD profiler bottom in order to prevent sediments from fouling the sensors, and toalso allow the CTD profiler to sample to a constant 0.5 m from the bottom during each cast.The CTD pressure variable was converted to a depth via a correction factor obtained from thecomparison of the boat winch ‘wire out’ reading at the bottom of the casts and the bottom pressurereading from the CTD; this conversion factor was 1.0137 m/dbar. To compare the profiles obtained4See http://www.seabird.com/sbe25-sealogger-ctd.14 33.50’  33.00’  124oW  32.50’  32.00’  31.50’  56’  57’  58’  59’   50oN   012 km2012 CTD2013 CTD2014 CTD2015 CTDMooringFigure 2.3: The locations of the CTD profiles taken during the 2012 - 2015 CTD surveys, andthe October 2014 mooring.15Jun 2012 Sep 2012 Dec 2012 Mar 2013 Jun 2013 Sep 2013 Dec 2013 Mar 2014 Jun 2014 Sep 2014 Dec 2014 Mar 2015 Jun 20158383.58484.58585.5Lake Level [m above reference]Figure 2.4: Powell Lake heights above their reference level, obtained by Brookfield Renew-able Power at the site of the dam. CTD survey dates shown as circled red points, andmooring duration indicated by dashed box.from various years, the depth data was corrected for the varying lake surface heights using a dataset provided by Brookfield Renewable Power (Figure 2.4).In order to save time, only depths between 250 m and the bottom were measured with theprofiler, and it was kept at a depth of 250 m while the boat was maneuvered to the next samplinglocation. This ‘tow-yoing’ method became inefficient for sampling station spacings greater than500 m, and was not possible when more accompanying sensors were attached to the CTD, whichhad the effect of draining the memory and battery life at a quicker rate. In these situations (whichoccurred mainly during the 2015 survey), the CTD profiler would be brought back up to the surfaceafter each cast, so that the batteries could be replaced and data downloaded as necessary.2.3 Temperature Sensor and Current Meter MooringA mooring was deployed in the central section of the lake from late October to early December2014 (Figure 2.3, Figure 2.4). The mooring was instrumented with 38 temperature sensors and 2current meters (Figure 2.5). The temperature sensors used on the mooring were the SeaBird SBE565, RBR Solo 6, and RBR TR10507; the current meters used were InterOcean Systems Inc. S4ACurrent Meters8. Upon retrieval, it was discovered that one of the 38 temperature sensors used onthe mooring had stopped functioning due to a leak from a faulty O-ring. All other components werefunctioning properly upon retrieval.Thirty-six of the temperature sensors were attached to a rigid plastic beam in a 2 metre verticalline array with 18 of the sensors spaced 7 cm apart in the top of this section and 18 sensors spacedat 3.5 cm apart on the bottom. This spacing was chosen after examining results from a previousmooring deployment in Powell Lake by Scheifele (2013) in which sensors were spaced 14 cmapart. The other two temperature sensors were positioned such that one was placed on the acoustic5See http://www.seabird.com/sbe56-temperature-logger.6See http://www.rbr-global.com/products/small-single-channel-loggers/temperature-rbrsolo-t.7See http://www.rbr-global.com/products/dual-channel-loggers/temperature-a-depth-rbrduo-td.8See http://www.interoceansystems.com/s4specs.htm.161 m 0 m 3 m 2 m 5 m 4 m 7 m 6 m 9 m 8 m 28 m 10 m 30 m 29 m 31 m Float Rope 1 SBE 56 Temperature Profiler Rope InterOcean S4A Current Meter  InterOcean S4A Current Meter  Rope 18 SBE56 Temperature Profiler (7 cm spacing) 18 RBR Solo Temperature Profiler (3.5 cm spacing) Rope Rope InterOcean Model 111 Shallow Water Acoustic Release  + 1 RBR TR1050 Temperature Profiler Chain Weights Figure 2.5: A schematic of the mooring deployed between October and December of 2014,showing the location of the 2-m vertical line array of temperature sensors with currentmeters above and below, and the location of the other two temperature sensors.17release 1 metre from the mooring bottom, while the other was attached to the line 1.5 m below thefloat, in a region with a linear temperature gradient.The RBR Solo temperature sensors were set to a sampling rate of 2 s−1, whereas the SBE56and RBR TR1050 temperature sensors were set to a sampling rate of 1 s−1. All sensors had atemperature resolution of 0.1 m◦C, with an electronic noise level of ± 0.2 m◦C. After the mooringwas retrieved, the temperature sensors were all placed in a calibration tank to inter-compare theirreadings while bringing the temperature of the calibration bath to values found in the lake. Thesensors showed offsets of up to 1 m◦C from the mean reading, with a slight dependence of thisoffset on the temperature of the bath. The moored temperature data were corrected by removing themean offsets for each sensor.The two current meters were positioned one above and one below the 2 metre section of temper-ature sensors. These current meters function by creating an AC magnetic field and then reading theinduced potential associated with the flow of salt water (a conductor) through that field, across twoperpendicular sets of electrodes (Lawson et al., 1983). The magnetic field may be disturbed if thereare other conductors nearby, and so the current meters were spaced 1 meter apart from the nearesttemperature sensors to minimize these disturbances.The current meters were set to record 1 minute-averaged currents once every 6 minutes, andinstantaneous heading and tilt once every 30 minutes. Calibration tests were performed both beforethe deployment and after retrieval of the mooring. This involved testing the out-of-water headingresponse, and the in-water speed and direction response to oscillatory motion and rest. The calibra-tion showed that both sensors had a heading resolution of 1◦ and a tilt dependent bias of ± 3◦; bothsensors had a speed resolution of 2 mm/s. While running on the 2 second-average setting the noisein the speed readings of the instruments was observed as a variability of ± 2 mm/s in the signal, inaccordance with manufacturer specifications; however, the instrument manual indicates that for the1 minute-average setting the noise level would be below the measurement resolution.The tilt record on both current meters stayed fairly consistent between 0−1◦, indicating that themooring remained almost vertical and hence sampled the same depths at all times. The instrumentheading also remained fairly constant except for a slow drift over the first two weeks (not shown).However, raw current speeds of the upper current meter were consistently larger than those of thelower current meter throughout the entire mooring deployment. This difference appeared to driftfrom about 3 cm/s to 5 cm/s over the first few weeks of deployment, and then stabilized for theremainder of the deployment (Figure 2.6, top left). Neither the strength nor the direction (notshown) of the long term trends in the currents seemed reasonable, and the drift seen in the initialweeks of the deployment also suggested some instrumental problem.During the calibration tests done after the mooring was retrieved, the zeros on the current meterswere seen to differ by up to 2 mm/s between tests where the lake residue was left uncleaned on theelectrodes and after it was wiped off with alcohol. The long term drift observed in the raw currentswas still far greater than this difference, and so, unlikely to be caused purely by the buildup ofcompounds from the lake water onto the electrode surfaces. The pre- and post-calibrations were18Figure 2.6: Top Left: The 18 minute mean current speeds measured by the lower (blue) andupper (red) current meters during the period of the mooring deployment, with the longterm trends shown in black. Top Right: The deviations from the long term trends, withmajor axes in the 131◦ direction for the lower current meter and 139◦ for the uppercurrent meter. (East is 0◦ and North is 90◦) Bottom Left: The current deviations alongthe major axes over the course of the mooring deployment. Bottom Right: The enhancedresponse of the upper current meter (S4b) relative to that of the lower (S4a), shown as aslope greater than 1:1 (black line).performed in salt water, but not with the exact composition of the waters at the bottom of PowellLake, such that any junction potential effects between the electrodes and the anoxic deep waters ofPowell Lake would not necessarily be reproduced.An attempt was made during the 2015 CTD survey to determine whether the difference in thelong term signal between the two current meters was a feature of the velocity structure withinthe lake or simply a sensor issue. This was done by profiling the current meters (much like theCTD profiler) so that both current meters would profile the same vertical regions within the lake at(nearly) the same time. Contamination of this data by the motions of the boat, however, made thetests inconclusive.Although the validity of the long-term trends within the currents remains in question, it wasdecided that these trends should be removed and only the shorter-period deviations be considered in19subsequent analysis. Note that the correlation of what seem to be advective features in the temper-ature record with these current deviations strongly suggest that the mean currents, in this stagnantbottom water, are in fact very close to zero (<∼0.5 mm/s).The current deviations formed an elongated region of scatter, with the major axes being 131◦for the lower current meter and 139◦ for the upper current meter– both in the northwest direction.This direction is not entirely aligned in the along-lake direction, possibly due to the interaction withthe bottom topography, but shall nonetheless be referred to as the along-lake direction.The variability in the current records were highly correlated (Figure 2.6, bottom left); however,the upper current meter consistently recorded slightly stronger variations than observed by the lowercurrent meter (Figure 2.6, bottom right). It is unclear whether this difference is due to real verti-cal shear in the water column or sensor sensitivities as the currents were much smaller than themanufacturer accuracy specification (±1 cm/s). As such, all that was concluded about the verticalstructure was that the two were highly correlated.20Chapter 3Analysis and ResultsThe types of data acquired for this work were varied in nature, encapsulating the wide range oflength and time scales involved in DD processes and their associated staircase structure. Accord-ingly, the analysis of the data varied equally and was divided into three distinct approaches: theidentification of the layer structure of the DD steps, and the evaluation of the horizontal coherenceand temporal evolution of this structure; the identification and subdivision of the motions presentwithin the lake which apply to the large scale DD structure and to the small scale DD step; and theidentification of a single DD step and the dynamics within it.3.1 Structure and Dynamics of DD LayersIn order to identify individual steps in the temperature and salinity profiles from the CTD data, anapproach similar to that of Polyakov et al. (2012) and Scheifele et al. (2014) was employed. Thisrequired identifying the transition regions between the high-gradient diffusive interfaces, the step“treads”, and the near-uniform convective regions, the step “risers”.To identify these features, the temperature and salinity profiles were first smoothed with a 15 cmrunning mean filter to eliminate the small-scale variability due to instrument noise. A backgroundprofile was then constructed by applying a 2 m running mean filter to the data to smooth out thefeatures of the DD steps. The difference between the smoothed and background profiles showedpeaks that correspond to the transition regions between the diffusive interfaces and the convectiveregions (Figure 3.1). These transition points were more evident in the temperature profiles than thesalinity profiles, and thus the former were used to isolate the step risers. Only step risers which weretaller than 15 cm and that contained temperature variations less than 1 m◦C in the smoothed profileswere retained, since any features with smaller vertical extents and larger temperature variations thanthis more closely resembled the step treads.In order to combine the identified risers from individual profiles into spatially coherent layers,an analysis procedure was created combining two different approaches used to identify DD layersin past studies. The approach taken by Padman and Dillon (1987) and Schmid et al. (2010) wasto compare a certain property of the risers from adjacent profiles; the risers whose properties were219.305 9.31 9.315 9.32 9.325336337338339340341In−Situ Temperature [oC]Depth [m]16.622 16.624 16.626 16.628 16.63336337338339340341Reference Salinity [g/kg]Depth [m]−2 −1 0 1 2336337338339340341Depth [m]∆ S [mg/kg] and ∆ T [moC]Figure 3.1: Left to right: The 15-cm running mean smoothed (blue) and 2-m running meanbackground (black) in-situ temperature profiles; the smoothed (red) and background(black) reference salinity profiles; and the differences between the smoothed and back-ground temperature (dashed blue) and salinity (dashed red) profiles. Shown are typicalexamples for illustrative purposes only, with the transition points between convective re-gions and diffusive interfaces marked with filled circles and the mean riser propertiesshown with open circles.closest in the adjacent profiles were combined to form a single layer. In contrast, Timmermanset al. (2008) and Scheifele (2013) suggested that individual layers would form distinct clusters ona temperature-salinity (T-S) plot, and thus could be identified by looking at all of the CTD profilestogether in this way. Combining the two methods, an algorithm was created that would matchrisers from adjacent profiles into layers, according to a criterion that would produce clusters ina temperature-salinity plot which were most agreeable with a visual inspection. Examining thevarious clustering criteria options (eg. possible combinations of mean riser salinity, temperature,density, or depth) indicated that matching closest profile-to-profile mean riser salinity produced thebest results.The layer finding algorithm successfully identified around 25 layers per survey in the lowest DDactive region of the lake. These layers appear as discrete clusters on T-S diagrams (Figure 3.2). Theclusters appear tightest in a central region of the T-S diagram, and begin to overlap or spread out inregions further away from the center. These clusters have an elongated shape, with the slopes of theclusters not aligned along isopycnals, indicating that the density in individual layers is not constantalong the lake.2214.145314.150514.150514.155814.155814.16114.16114.16114.166214.166214.171414.171414.176614.176614.181814.181814.18714.18714.1922Reference Salinity [g/kg]In−Situ temperature [oC]16.52 16.53 16.54 16.55 16.56 16.579.269.289.39.329.349.36(a)14.145314.150514.150514.155814.155814.16114.16114.16114.166214.166214.171414.171414.176614.176614.181814.181814.18714.18714.1922Reference Salinity [g/kg]In−Situ temperature [oC]16.52 16.53 16.54 16.55 16.56 16.579.269.289.39.329.349.36(b)14.145314.150514.150514.155814.155814.16114.16114.16114.166214.166214.171414.171414.176614.176614.181814.181814.18714.18714.1922Reference Salinity [g/kg]In−Situ temperature [oC]16.52 16.53 16.54 16.55 16.56 16.579.269.289.39.329.349.36(c)14.145314.150514.150514.155814.155814.16114.16114.16114.166214.166214.171414.171414.176614.176614.181814.181814.18714.18714.1922Reference Salinity [g/kg]In−Situ temperature [oC]16.52 16.53 16.54 16.55 16.56 16.579.269.289.39.329.349.36(d)Figure 3.2: The DD layer clusters in T-S space shown with contours of potential density[kg/m3] computed with a reference at 325 dbar. Individual layers are shown as differentcoloured clusters for the a) July 2012 data, b) June 2013 data, c) May 2014 data, and d)June 2015 data. Dashed box region shows the central portion of the steps with the mostcoherent properties.A potentially useful characteristic of the clusters is the horizontal density gradient (Timmermanset al., 2008), defined as:Rρx ≡ β∂S/∂xα∂T/∂xwhere α and β are the thermal expansion and saline contraction coefficients, and ∂S/∂x and ∂T/∂xare the horizontal temperature and salinity gradients, respectively. The horizontal density gradientcan be thought of as a normalized slope on the T-S diagram. The survey means and populationstandard deviations of the horizontal density gradient, from the layers within the central region onthe T-S diagram, were found to be -0.12±0.27 in the 2012 survey, -0.29±0.36 in the 2013 survey,-0.02±0.37 in the 2014 survey, and -0.31±0.34 in the 2015 survey. Thus, scaled horizontal salinityvariations are small in comparison to the horizontal temperature variations.2349.94 49.96 49.98330332334336338340342344346348350Depth [m]Degrees Latitude [o]2012 Survey49.94 49.96 49.98Degrees Latitude [o]2013 Survey49.94 49.96 49.98Degrees Latitude [o]2014 Survey49.94 49.96 49.98Degrees Latitude [o]2015 SurveyFigure 3.3: The depths and vertical thickness of the DD layers found in each survey. Coloursindicate the layers matched up from year to year and the region between dashed linesindicate the central layers with the most coherent properties. Both the colours and theboxed region are consistent with those shown in Figure 3.2. Mooring location is shownas black ellipse in 2014 data.The horizontal extents of the layers (Figure 3.3) indicate that many of the layers are coherentover the entire sampling domain of roughly 9 km, especially in the depth range of 336 m to 347m. This region corresponds to the central region in the T-S diagrams, where the clusters are mostevident. This section of the water column is characterized by near constant values of the verticaldensity gradient, Rρz = 2.2±0.2, and buoyancy frequency, N = (2.3±0.3)×10−3 s−1 (Figure 3.4).Above and below this depth range, the layers appear less coherent along the lake, clusters on T-Sdiagrams appear less compact, and the vertical density ratio and buoyancy frequency increase fromtheir central region values. Although the Rayleigh number, Ra, has a maximum of ∼ 107 in thecentral region, vertical variations in Ra do not correlate in an obvious way with the structure of Rρzor N (Figure 3.4).Variability in the depths of individual layers appears to be similar in neighbouring layers aboveand below. An example of this can be seen with the roughly 0.5 m rise in the layers present arounda latitude of 49.97◦ in both the 2012 and 2015 surveys (Figure 3.3). There also exist sections inwhich layers appear to terminate away from the side boundaries. The most evident case of this canbe seen with the layer around a depth of 345 m, which is bound by the layers above and below it,and terminates at a latitude of just under 49.96◦. This layer termination can be seen in the 2012,2013, and 2015 surveys; the 2014 survey did not capture data at this latitude.The corresponding properties of the layers (Figure 3.5) indicate that the salinity is almost uni-form along layers, consistent with the almost vertical clustering in Figure 3.2, whereas the tem-perature and density show consistent along-lake trends in their structure. The trends of the layer24Figure 3.4: Left to right: The background vertical density gradient, Rρz, buoyancy frequency,N, and Rayleigh number, Ra, of all of the profiles from the 2012-15 surveys. Values ofRρz and N are almost constant with depth in the central region between 336 m to 347 m.This structure is not visible in the Ra profile.properties are most coherent among layers between depths of 336 m to 347 m, and less coherent inthe layers outside of this central region.Due to the consistency of the depth and temperature properties of the layers, it was possible toidentify the same layers from year to year. This year-to-year existence of the same layers can beseen as consistent colours present in Figure 3.3 throughout each of the surveys, with unmatchedlayers left uncoloured. Once again, the layers in the central region were the most consistent; theirproperties did not change significantly from year to year, and the layers were identified with ease insuccessive years. In contrast, the layers above and below this region showed much more variationfrom year to year and were more difficult to track. The location of the October of 2014 mooringindicates that it was deployed in a region where the layers were relatively stable.The deviations of the layer properties from their mean values were calculated in order to moreclearly compare the layers from year to year. Deviations were first calculated for each layer, andthen these deviations were averaged together for each survey (Figure 3.6). The mean deviations hadto be shifted by +1 m◦C in temperature, -0.2 mg/kg in salinity, and -0.3g/m3in density to visuallyalign with the results of the 2012 and 2015 surveys. The need for these shifts is attributed to thefact that the 2013 and 2014 surveys did not sample as much of the lake (horizontally), relative tothe 2012 and 2015 surveys.Linear least squares fits to the layer property deviations showed a general trend with layersgetting colder by 2 m◦C, more saline by 0.1 mg/kg, denser by 0.4 g/m3, and deeper by 0.4 mfrom the southern to the northern ends of the 9 km lake bottom. These layer property variations2516.5216.52516.5316.53516.5416.54516.5516.55516.5616.565Reference Salinity [g/kg]2012 Survey9.279.289.299.39.319.329.339.349.359.36In−Situ Temperature [o C]49.94 49.96 49.981014.111014.1151014.121014.1251014.13Potential Density [kg/m3 ]Degrees Latitude [o]2013 Survey49.94 49.96 49.98Degrees Latitude [o]2014 Survey49.94 49.96 49.98Degrees Latitude [o]2015 Survey49.94 49.96 49.98Degrees Latitude [o]Figure 3.5: Top to bottom: Reference Salinity, in-situ temperature, and potential density(with a reference of 325 dbar) of the identified DD layers in each survey. Thicknessesof layer properties indicate the range of values between the lower and upper boundary ofthe step risers. Layer colours and central region between the dashed lines are consistentwith those shown in Figure 3.2 and Figure 3.3..26−505∆ T [moC]−0.500.5∆ S R [mg/kg]−0.500.5∆ ρ [g/m3]49.94 49.95 49.96 49.97 49.98 49.99−101∆ Depth [m]Degrees Latitude [o]Figure 3.6: Top to bottom: Deviations of in-situ temperature, Reference Salinity, potentialdensity, and depth of the layers from their layer mean values, averaged over all of thevertical layers in each survey. July 2012 survey shown in blue, June 2013 shown in red,May 2014 in green, and June 2015 in black. Error bars show the range of 1 samplestandard deviation.were smaller than the mean property differences between vertically adjacent layers (≈ 4 m◦C and 2mg/kg). Using the least squares fits to the temperature and salinity gradients, the horizontal densitygradient, Rρx, was found to be -0.35±0.17 – an alternative approach to computing Rρx by meansof identifying the slopes of the layer clusters on a T-S plot. This approach is more reliable thanthe former since it incorporates the full horizontal extent and temporal evolution of the layers in itscalculation.3.2 Motions Within the LakeThe major feature of the observed currents were oscillations with a period of approximately 21hours, with times of higher and lower activity over the deployment (Figure 3.7). The first fewdays of the mooring deployment showed high activity, followed by a calm period at the end ofOctober/beginning of November. This was then followed by another high activity period of varyingamplitude between November 2nd and November 10th. The least variable currents were observedbetween November 12th and 22nd , after which they became more active once again.27−50050Wind Speed [km/h]9698100102Air Pressure [kPa]Oct−26 Oct−31 Nov−05 Nov−10 Nov−15 Nov−20 Nov−25 Nov−30 Dec−05−101Lake Currents [cm/s]Figure 3.7: Top to bottom: Wind speed in the major axis direction of 165◦ (from the north-west); the air pressure; the lake horizontal currents speed obtained by the lower (blue)and upper (red) current meters with long term trends removed, 5-10 m above the lakebottom.Wind and air pressure records were obtained from a government weather station at Powell Riverairport. The lake is roughly 10 km from the airport and surrounded by mountains on all sides, sothat the airport records are probably not a good representation of the conditions over the lake. Thewind and pressure data, however, showed similar trends in activity as those observed in the currents(Figure 3.7). More active winds and lower atmospheric pressures are seen around the time thatthe lake currents are most active, and higher pressures and calmer winds around the time when thecurrents are most quiet. There is also a time lag of a few days between changes in the activity ofthe winds/air pressure and the currents, which is likely due to inertia in the response. An analysis ofthe internal seiche modes present in the lake (not shown) suggested that the large current variationswere most likely caused by wind activity coupling to an internal seiche mode with a period ofapproximately 21 hours. Maximum currents associated with the seiche activity are on the order of1 cm/s.In addition to the horizontal currents record obtained by the current meters, the arrangementof the temperature sensors on this mooring provided further information about the horizontal andvertical lake motions. The temperature record of the sensor located at 322 m depth, in a region ofconstant temperature gradient, varied in temperature by roughly ±0.05◦C, and in a manner similarto that of the currents obtained from the current meters (Figure 3.8, top right and Figure 3.7, bottom).Since this sensor was in a region which was not DD active, the temperature gradient was nearlylinear and could be used as a conversion between observed temperature and the vertical motion ofthe water column. The inferred motions showed vertical displacements of up to a metre above andbelow the initial depth (Figure 3.9, top), with similar variability as the horizontal displacements (ofunder 50 m) obtained from the integration of the along-lake currents (Figure 3.9, middle). Thesenorthward and downward (southward and upward) motions are highly correlated, which is consis-288.6 8.8 9 9.2 9.4310315320325330335340345350In−Situ Temperature [oC]Depth [m]8.858.98.959Temperature [o C]9.339.3359.349.3459.35Oct−28 Nov−07 Nov−17 Nov−27 Dec−079.359.369.379.38Figure 3.8: Left: The temperature profile of the bottom 40 m of the lake taken with the CTDprofiler just before mooring deployment, indicating the locations of the three sections oftemperature sensors (red circles). Right: The temperature record from: the temperaturesensor at the 322 m depth (top); the middle temperature sensor on the 2 m long array oftemperature sensors at a depth of 344 m (middle); the temperature sensor attached to theacoustic release, at a depth of 349 m (bottom).tent with a seiche mode. The coherence spectrum of the two records (not shown) showed strongcoherence in-phase in the 13-27 hour period range.The temperature sensor on the acoustic release, 1 m above the lake bottom, showed temperatureoscillations on the order of ±0.03◦C, similar to those seen at 322 m but with a varying long termtrend (Figure 3.8, bottom right). This temperature series still exhibited the near daily oscillationscommon to the 322 m temperature sensor data and the current meter data, and showed a calm periodwith a peak temperature just after November 17th, near the end of the period when the currentdeviation data showed the lowest activity.Since the vertical motions near the lake bottom are presumably minimal and the geothermalheat flux is assumed to be constant in time over the sampling domain, the most likely remainingpossibility for such temperature changes near the lake bottom would be a result of the horizontaladvection of water with different temperatures. In order to match the scales of horizontal displace-ments inferred from this bottom temperature record with those obtained from the current meters, ahorizontal temperature gradient of -0.1 m◦C/m was assumed in the direction of motion (Figure 3.9,29−2−1012Vertical Displacement [m]−150−100−50050100Horizontal Displacement [m]Oct 28 Nov 02 Nov 07 Nov 12 Nov 17 Nov 22 Nov 27 Dec 02−1000100200Horizontal Displacement [m]Figure 3.9: Top to bottom: Inferred vertical displacements of the temperature sensor at 322m depth, using the CTD profiler data from the same region; the horizontal displacementof the lake water from the integrated currents from the lower (blue) and upper (red)current meter records; the possible horizontal displacement of the lake water from thetemperature sensor at 349 m depth, assuming a horizontal temperature gradient of -0.1m◦C/m in the along-lake direction (northwest).bottom) – along the major axis of the currents. This assumed horizontal temperature gradient is afactor of ∼ 300 greater than the one obtained by looking at the four year mean temperature gradientwithin layers, which is roughly −3×10−4 m◦C/m (Figure 3.6).3.3 Dynamics Within a DD LayerAs was shown in the previous section, the mooring was regularly subjected to seiches on time scalesof around a day. A vertical displacement of about 1 m at 30 m above the bottom suggests a verticaldisplacement of around 20 cm at 6 m above the bottom, but the observed vertical changes in thevertical temperature array are larger than this. These motions made it difficult to identify any DDsteps in much of the temperature data (Figure 3.10, top) since these steps migrate outside of thesampling domain on a daily basis.Also note that, although the temperature sensors were all corrected using calibration data, smalloffsets on the order of 0.5 m◦C were still visible (Figure 3.10, top). These offsets appeared through-out the time series in the form of horizontal banding. To correct for this, a hyperbolic tangentfunction was fit to each step where they were identified, and deviations from this fit were correctedlocally to remove these bands. This correction procedure was only applied when the time scale wason the order of a day and not more. Thus, the temperature data presented in Figure 3.10 still showsthe banding features, but these sensor-related features have been removed in subsequent figures.30Figure 3.10: The October-December 2014 mooring data showing the contoured, post-calibration-corrected temperature record with height from the bottom sensor (top), thepeaks of the temperature histogram time series (middle), and the 18-minute mean fil-tered currents in the along-lake direction from the lower (blue) and upper (red) currentmeters (bottom).In order to more easily identify the DD steps present within the moored temperature data, thetemperature time series was converted into a temperature histogram time series showing the dom-inant temperatures sampled at each time (Figure 3.10, middle). This method involved first inter-polating the temperature data at each time step with a stiff spline to obtain a temperature profilewith 1 cm vertical resolution, and then binning the data into 0.2 m◦C bins to produce a temperaturehistogram time series. Since the convective region of a DD step has a near uniform temperaturedistribution, these regions could be found by looking at bins with a high count in the temperaturehistogram. Thus, the peaks in this temperature histogram time series would indicate the mean tem-perature within the step risers of any DD steps present, while the number of peaks would indicatethe number of step risers, and thus the number of DD steps, present in the vertical-array data.The number and consistency of DD steps found in the temperature record are related to thestrength of the currents (Figure 3.10, bottom). During the first few days of the temperature record,when large oscillations occur in the horizontal current speeds, the steps appear and disappear repeat-edly (Figure 3.11a). During October 25th, between 12:00 and 21:00, no steps could be identifiedin the temperature data nor the temperature histogram peak data; the seiche currents are around 0.5cm/s in the along-lake direction at this time. Between 21:00 on October 25th and 03:00 on October26th, the currents reverse direction and four steps appear in both the temperature and temperaturehistogram data. Interestingly, the vertical position of the steps is affected by the two negative peaksin the currents just after 00:00 and around 02:30, producing a rise of nearly 50 cm of the steps.After 03:00 on October 26th the steps once again appear to disintegrate as the currents reverse di-rection once more. The appearance and disappearance of the steps can be seen to occur twice more31(a)(b)Figure 3.11: Periods in the moored time series when steps a) appear and disappear, and b)are fairly consistent in time, showing: the contoured temperature time series (top), thepeaks of the temperature histogram time series (middle), and the 3 point running meanfiltered currents in the along-lake direction (bottom).in the 2 day period shown in Figure 3.11a, each time following the motions of the currents. It istherefore possible that this variability is actually spatial, with regions of formed and destroyed DDsteps being advected past the mooring. Alternatively, since the mooring did not rotate during thedeployment and the temperature sensors were all arranged on one side of the mooring, the observedstep destruction could be the result of a wake generated by the presence of the mooring when thetemperature sensors were facing down-stream of the currents.Later in the mooring deployment, three steps could be consistently identified (Figure 3.11b).The formation of these three steps happens around the same time that the temperature maximum isreached in the bottom temperature sensor attached to the acoustic release – around November 17th.During this period, the currents are weak, with speeds below 0.2 cm/s in magnitude, resulting inhorizontal displacements of under 50 m. The steps migrate vertically by up to 50 cm during thisperiod, but stay well defined in the temperature and temperature histogram data.Since it allowed for the full identification of the middle step, bounded by the ones above and32(a)9.3369.3389.349.342Temperature [o C]00.511.5Thickness [m]Nov 18 Nov 19 Nov 20 Nov 21 Nov 22 Nov 23 Nov 24 Nov 25−0.500.5Depth Deviation[m](b)Figure 3.12: a) Location of a single DD step by means of isolating the step temperature (redline) using the temperature histogram time series (top), and then locating the corre-sponding upper and lower step boundaries (black lines) using the temperature time se-ries (bottom). b) The evolution of the DD step properties for the period of time that thestep was tracked.below, this region was therefore used for the purposes of tracking the evolution of a single DDstep. The central histogram peak was isolated, and the upper and lower limits of the step riser werelocated by identifying the places in the temperature time series (Figure 3.12a) where the temperaturedeviated by more than 1 m◦C from the mean riser temperature. The step ‘thickness’ was definedto be the vertical distance between the upper and lower diffusive interfaces, and the step ‘depth’ asthe mean of the depths of the two interfaces. During these 8 days the temperature of the step riserdecreased by ∼ 0.1 m◦C, the depth stayed fairly consistent but fluctuated by up to ±0.5 m, and thethickness increased from ∼ 50 cm to ∼ 90 cm before decreasing again (Figure 3.12b).Although the horizontal velocities were not zero during this time, this period was the best timewithin the entire temperature record to examine processes in a reference frame fixed to the watermass in the step. In order to further understand the processes occurring within the DD step, thepower spectra of the step riser properties and currents in this time period (between November 17th33Figure 3.13: The variance preserving power spectra of the horizontal velocities and the DDstep properties using the multi-taper method. Shaded regions show the 95% confidencelimits. A common peak (shown within the boxed region) with a frequency of 2.73 cphis visible in the step temperature, currents, and step thickness.and 25th) were computed by means of the multi-taper method (Figure 3.13). Although most of thevariance in the data was found to occur in the low frequency regions (small seiche related motions),a common peak was observed in the high frequency end of the riser temperature, horizontal currentspeeds, and (not as strongly) DD step thickness spectra. This common peak had a frequency of∼ 2.7 cph, resulting in a period of ∼22 minutes. This peak was not visible in the power spectrumof the depth of the step, implying that it is likely related to motions within the step (rather than ofthe entire staircase).In order to see whether any features were visible on the time scale of the common peak foundin the properties’ spectra, the mean temperature record was band-pass filtered to isolate the 22minute spectral peak (Figure 3.14), and two 6 hour regions were examined closely to show contrastbetween periods when the amplitude of the 22 minute signal was high (Figure 3.15a) and low(Figure 3.15b) (referred to as ‘active’ and ‘less active’ regions in what follows). Within the moreactive period in Figure 3.15a, higher temperature features are seen to appear periodically withinthe convective region of the step, either stretching from the bottom diffusive interface or appearingisolated in the centre of the convective riser; the less active period in Figure 3.15b does not showsuch features. This observation helps support the idea that the 22 minute spectral peak correspondsto thermal plumes within the convective riser, since such features are visible when the band-passedmean temperature signal is higher, and not visible when it is lower. During the 6 hour period on3400.10.20.30.40.5Temperature [moC]Nov 17 Nov 18 Nov 19 Nov 20 Nov 21 Nov 22 Nov 23 Nov 24 Nov 25−50050Horizontal Displacement [m]Figure 3.14: Top to bottom: The 22 minute band-pass filtered, mean temperature record fromthe 2-m vertical array, with the two chosen 6 hour periods (described in the text) indi-cated by dashed boxes; the horizontal displacement associated with the horizontal lakevelocities from both current meters (upper current meter in red, lower current meter inblue).November 21st , there were roughly 15 of these plume structures, appearing once every 24 minutes.There was an asymmetry to the appearance of these plumes, such that warm plumes were con-sistently observed to extend upwards from the bottom diffusive interface, but no cold plumes wereseen to extend downward from the upper diffusive interface. The plumes appear to (occasionally)have an effect on the layer thickness, stretching it upwards upon reaching the upper diffusive inter-face. This could explain the presence of the weaker (22 minute) peak in the step thickness powerspectrum. At times, when powerful enough, the plumes appeared to penetrate into the step aboveand continue upwards (Figure 3.15a, around 07:00).The variation in the band-pass filtered temperature record suggests that the plumes are intermit-tent features. It is possible that the plume formation is fixed spatially and that the advection of thewater past the mooring (which is small but still non-zero) captures these sites periodically. However,no obvious correlation is present between inferred horizontal displacements and the strength of theband-passed mean temperature signal (Figure 3.14). Thus, it appears more likely that the variabilityis due to a temporal component rather than due to the advection of features from variable formationsites.Based on the mean values of the band-passed temperature and horizontal velocity (not shown)records, the plume temperature anomaly and horizontal velocity scales were estimated as T ′ ≈ 0.2m◦C and u′≈ 0.5 mm/s, respectively. Furthermore, by taking the∼22 minute period of these plumesand the mean height of 0.6 m of a single DD step in this period, a vertical velocity scale of w′ ≈ 0.5mm/s can be inferred.35(a)(b)Figure 3.15: a) & b): The temperature profiles (left) as a function of distance from the bot-tom diffusive interface, at the initial time of the 6-hour close-ups (left) of the contouredtemperature time series, when the DD step is clearly visible. Step boundaries are iden-tified in purple, with the bottom interface fixed vertically in place to emphasize motionsinternal to the DD step.36Chapter 4Discussion and Future WorkThe diffusive mode of double-diffusive convection has been studied extensively using numerical andlaboratory models. However, observations in natural systems have, in many ways, lagged behind.The present work addressed this gap by using observational data from the natural environment inPowell Lake, which allowed for a novel observation and characterization of the spatial and temporalprocesses of and within naturally occurring double diffusive layers.The data attained from four annual surveys of vertical CTD profiles showed roughly 20 double-diffusive layers which were horizontally coherent throughout the entire lake and persistent over thefour years. The moored temperature and horizontal velocity data revealed the presence of plume-like features in the convective region within an individual DD layer.4.1 Convective Regime Within DD LayersPrevious laboratory studies have indicated that the convective regime within double diffusive stepsvaries depending on the local value of Rρ , such that for 1<Rρ 6 2 the step is dominated by turbulentconvection/mechanical mixing, and for Rρ > 2 by intermittent thermal plumes emerging from thediffusive interfaces (Crapper, 1975; Lavery and Ross, 2007) (see also Figure 1.2). Furthermore,it has been shown that the thickness of the diffusive interface has a tendency to increase for evenhigher values of Rρ (Marmorino and Caldwell, 1976; Ross and Lavery, 2009), suggesting that thethermal plumes become weaker with increasing Rρ .Similar observations were made in numerical studies of the phenomenon, indicating that theconvection regime consists of intermittent convective instabilities for Rρ > 2 (Linden and Shirtcliffe,1978), with three-dimensional effects (a signal of fully turbulent convection) only becoming presentfor Rρ 6 2 (Flanagan et al., 2013). Direct numerical simulation by Carpenter et al. (2012) indicatedthe presence of plume-like instabilities (at Rρ = 3) which formed in the boundary layers of thediffusive interface.In most laboratory studies the existence of thermal plumes has only been hinted at by the ob-servation of fluctuations in the temperature signals (Turner, 1968; Marmorino and Caldwell, 1976;Newell, 1984). In previous observational studies of naturally occurring DD structures, although37there have been indications that the DD steps are indeed in a state of convection (Zhou and Lu,2013; Schmid et al., 2010), the similarity of the convective regime to that observed in laboratoryand numerical studies has only been suggested (Padman and Dillon, 1987). Thus, the observationsin the present study provide a detailed comparison between laboratory/numerical studies and geo-physical observations of the convective regime within individual steps, and help validate some ofthe results of those studies.Although it is observed that Rρz > 2 for the majority of the CTD profiles (Figure 3.4, left),roughly 6% of the data falls in the Rρz 6 2 regime within the central depth range (between 336 mand 347 m). If the results from laboratory and numerical studies can be applied here, this wouldsuggest that the majority of the DD layers in Powell Lake are stable in form, and are in a state ofconvection governed by intermittent thermal plumes, with occasional instances of more turbulentconvection present within the layers at depths between 336 m and 347 m. This variability in theconvective regime is consistent with the suggestion by Huppert (1971) that the stability (and thusthe convective regime) of the DD layers is based on local conditions only, and so can vary fordifferent locations within an individual layer.The mooring was located in the central depth range, ideally placed to test this hypothesis. How-ever, due to the presence of large-scale horizontal motions on the order of tens of metres (Figure 3.9)– which are most likely due to seiche activity produced by diel winds (Figure 3.7) – the mooredinstruments observed different regions within the lake throughout the sampling period. The factthat the layers appear clearly at some times and not others during the sampling period (Figure 3.11)suggests that either certain locations within the layer may be experiencing more active states of con-vection than others, or possibly that the presence of the mooring created occasional wakes whichwere able to disrupt the staircase structure. The spatial distributions of these regions could not beidentified, however, because of the essentially one dimensional perspective provided by the mooreddata.Luckily, the calm conditions during the period of November 17th to 25th, during which horizon-tal motions were minimal and a DD step could be observed consistently (Figure 3.10), allowed fora study of the dynamics within an individual DD layer (Figure 3.12)1. Of specific interest were thepower spectra of the mean temperature within the convective region and the currents at this time,which show a common peak with a period of ∼ 22 minutes (Figure 3.13). Unfortunately, the tem-perature and velocity signals could not be correlated directly because of the vertical offset betweenthe location of the temperature sensors and current meters, but the agreement in periodicity suggeststhat the phenomena being captured are the same.A common peak in the velocity and temperature spectra was also seen in a laboratory studyof single component thermal convection by Qiu et al. (2004). In this study, the spectra of tem-perature and velocity fluctuations at various points within a thermally driven convection cell wereanalyzed and a common peak was shown to exist, which was a result of the motions of the ther-1A key assumption here, based on the calm conditions, is that the observed variability in the step properties areassociated mostly with temporal effects rather than horizontal movement of the reference frame.38mal plumes responsible for driving the convection within the cell. Extrapolating these results fromsingle component convection to the two component case leads to the interpretation of the commonpeak observed in this study as resulting from thermal plumes.The background buoyancy period, 2pi/N, for the region where the mooring was deployedequates to ∼ 46 minutes, which is a factor of 2 larger than the period of the 22 minute spectralpeak. The buoyancy frequency calculated only within the diffusive interface could be approximatedas NI ≈√H+hh N, where H is the height of the convective region within the step and h is the heightof the interface, and taking h≈ 20 cm and H ≈ 60, this results in NI ≈ 2N. The buoyancy period forthe diffusive interface only, 2pi/NI , would then equate to a value of ∼ 23 minutes, which is remark-ably near that of the 22 minute spectral peak. This result is in close agreement with the observationsof Marmorino and Caldwell (1976).Band-pass filtering the temperature signal around this spectral peak and comparing it to the con-toured temperature time series, it is observed that there appear plume-like features in the contouredtemperature data (Figure 3.15). More plumes are visible when the amplitude of the band-passedtemperature signal is larger, and less when the signal is smaller. The features in the contoured tem-perature data cannot be the result of the tilt of the mooring since the angle of the mooring neverexceeded more than 1◦ from the vertical. The features are also unlikely to be solely caused byadvected features since the 22-minute band-passed temperature record (which is an indicator ofplume strength) did not show any obvious correlation with the horizontal displacements at this time(Figure 3.14).A scale for the upward velocity of these plumes can be obtained by taking the quotient of thelayer height, ∼ 0.6m, and the plume period, 22 minutes, resulting in a velocity scale of w′ ≈ 0.5mm/s. A temperature scale for the plumes can be obtained from the mean value of the band-passedmean temperature signal, and results in a value of T ′ ≈ 0.2 m◦C. A similar procedure for the band-passed horizontal velocity time series results in a horizontal velocity scale of the plumes of u′ ≈ 0.5mm/s.Assuming that the known mean vertical heat flux, FH ≈ 27 mW/m2 (Hyndman, 1976; Scheifeleet al., 2014), is the resultant of plume activity only, and that the plumes’ intermittency can bemodelled by a sinusoid, results in a balance ofw′T ′2A′ ≈ FHρcPA (4.1)where the factor of 2 on the left side comes from integrating w′T ′ over one plume period, and A′and A are the cross-sectional areas associated with the plumes and the mean heat flux, respectively.Taking a typical value for the density to be ρ ≈ 1014 kg/m3, and the specific heat capacity of waterto be cP ≈ 4100 J/(kg◦C), results in A′/A ≈ 13%, indicating that the plumes cover ∼ 13% of thearea within the layers.394.2 Horizontal Coherence of DD LayersPrevious field observations of naturally occurring DD structures have indicated that staircase struc-tures are often persistent over years (e.g. Hoare (1968), Carmack et al. (2012)) with layers that canbe tracked horizontally for up to hundreds of kilometres in some instances (e.g Timmermans et al.(2008), Carmack et al. (2012)), but not in others (Sirevaag and Fer, 2012). The differences in theseobservations naturally leads to the question of what determines the horizontal coherence of thesestructures.The observed DD layers in Powell Lake are consistently coherent over the length of the lake(Figure 3.3) and are surprisingly persistent over the four years of study, with the same ∼ 20 layersidentified in all four surveys. Not only are the layers themselves consistent, but their properties alsoappear quite steady over the course of the study (Figure 3.6), with the layers appearing consistentlycolder, saltier, and deeper towards the northern portion of the lake.The horizontal coherence of the layers, however, is not the same at all depths. The central region(between 336 m and 347 m) consistently contains the most horizontally-coherent layers, spanningthe entire lake length. The layer clusters on a T-S diagram are tightest in this central region – afeature that is similarly observed with the T-S clusters from the layers in the arctic (Timmermanset al., 2008). This region also exhibits a near uniform background vertical density ratio, Rρz =2.2±0.2, and buoyancy frequency, N = (2.3±0.3)×10−3 s−1 (Figure 3.4, left); whereas the lesshorizontally-coherent layers both above and below this region show a larger value of Rρz and N.Although the layer height varies horizontally along the layers, no time-variable layer merging orsplitting is seen in the central region for the entire 4 year duration, suggesting that the layers arestable.The value of Rρz = 2.2±0.2 for the stable layers in the central region is consistent with predic-tions from laboratory (Turner and Chen, 1974) and numerical (Huppert, 1971) studies, where it wasobserved that the layers would be stable provided that Rρz > 2. Furthermore, due to the stabilityof the layers, it can be inferred that they are in a regime for where the density flux ratio, γ , is at aconstant value of∼ 0.15 (Radko, 2003). A typical value Rρz = 2 is accepted as the region for whereγ transitions into this constant regime (Turner, 1968).As the DD structure is in the intermittent plume regime of convection, and the strength of theplumes diminishes with increasing Rρz (Newell, 1984), this could explain why the top and bottomlayers (although still in the stable regime of Rρz) appear less coherent than those within the centralregion. The higher values of Rρz in the top and bottom DD layers would imply that the plumes areweaker there, and are less able to maintain well defined diffusive interfaces. As such, without thecontainment provided by strong plumes, the interfaces would be more prone to diffuse (vertically)outwards and erode away, thus destroying the horizontal coherence of the layers.Although layers become less coherent both above and below the central region, there are differ-ences between the characteristics of layers at the top and bottom. This is observed in the differencesbetween layer clusters in T-S diagrams, where the clusters associated with the top layers tend tohave a larger spread in temperature than those associated with layers at the bottom (Figure 3.2).40The cluster trends observed in the arctic study by Timmermans et al. (2008) show similarity tothose present at Powell Lake, which suggests that the horizontal coherence of the layers is variablein the arctic as well, with more horizontally-coherent layers sandwiched vertically between lesshorizontally-coherent layers.The difference between the two regions is further emphasized by the fact that the top layers aremore horizontally-coherent than those at the bottom, with the top layers typically having a singlebreak in the layer along the length of the lake, while bottom layers are more segmented (Figure 3.3).These differences between the layers may imply that Rρz alone is not enough to characterize theconvective regime within, and stability of, the DD layers. It was recently found by Scheifele et al.(2014) that (in the DD system in Powell Lake) for values of Ra& 106 and Rρz & 3, the ratio betweenthe total heat flux to conductive heat flux within a layer, given by the Nussult number,Nu=HFHρcPkT∆T(4.2)can be described as a decreasing function of Rρz; whereas for lower Ra and Rρz, Nu is dependentprimarily on Ra.The vertical variability of the layer Rayleigh number (Figure 3.4, right) indicates that the toplayers typically have a higher Ra than the bottom layers. The top layers have a mean Rayleighnumber of Ra > 106 and vertical density ratio of Rρz > 3, whereas the bottom layers have a meanvalue of Ra≈ 106 and 2< Rρz < 3. These differences may suggest that the top layers are in a regimewhere Nu is governed by Rρz and the bottom layers are in a regime where Nu is governed by Ra.A more complex description is also suggested by the numerical study of Carpenter et al. (2012),who indicated that the transition region from the convective regime to the double diffusive regime(and also into the stable regime) may have a dependence on the Rayleigh number. Carpenter et al.(2012) showed that the transition would occur at higher values of Rρz, for higher values of Ra. Thisleads to the conclusion that as Rρz is increased, in order to keep the convective regime constant, Rahas to be increased as well, and implies that when comparing layers with similar values of Rρz, thelayer with higher Ra will be in a stronger state of convection. The findings of Scheifele et al. (2014)are seemingly inconsistent with those of Carpenter et al. (2012), but for the purposes of the presentwork, the important aspect from both studies is that they both indicate that Ra is important for acomplete description of the convective regime within layers.Thus, it appears that the horizontal coherence of layers is dependent upon the convective regimewithin the layers, with the most horizontally-coherent layers having the lowest values of Rρz andhighest values of Ra, such that the convective regime is still within the region for where γ is constant.This possible Ra dependence on the convective regime may explain why the most coherent layersappear at higher values of Rρz in other studies, as in the case of Lake Kivu where the most coherentlayers are observed with values of Rρz ≈ 4 (T. Sommer, personal communication) and Ra ≈ 108(Sommer et al., 2013).The horizontally-coherence of the layers can be identified by observing the clusters formed on41T-S plots, because the most horizontally-coherent clusters will be associated with the clusters whoseproperties are well-separated from those of layers above and below. If the horizontal coherence isindeed determined by the convective state within the layers, this would imply that the convectivestate could also be determined solely by the properties of the clusters on T-S plots.4.3 Variability of DD Layer StructureIn laboratory studies of a salt stratified fluid heated from below, the DD layers that form are typicallyhorizontal with no overall slope. The layers observed in Powell Lake, however, show consistentvariations in their depths (Figure 3.3). Since there are no known sources of external waters (e.g.underwater springs) at these depths or anywhere around the lake, and the deviations of the layerproperties are consistent over time (Figure 3.6) – which implies that internal wave and seiche activityaliased over the sampling period are not the cause of this variability – it is likely that the observedlayer variability is mainly due to the slower double diffusive processes, perhaps in relation to spatialchanges in bottom geometry or heat flux.The identification of layers using closest profile-to-profile salinity to isolate the clusters presenton the T-S plot (Figure 3.2) indicates that that the layers tend to follow closely the contours ofbackground salinity. Within the layers, the horizontal buoyancy gradient due to temperature islarger than that due to salinity – that is, |β∂T/∂x|> |α∂S/∂x|, since |Rρx|< 1. It is interesting tospeculate whether this is related to the assumption that it is likely the temperature field that drivesthe variability within the layers at Powell Lake, and the salinity field only attempts to compensate.The variations in layer depth and the background temperature distribution are consistent over thestudy period, suggesting they are linked to one another (Figure 4.1).The depth variation of the layers appears to follow closely the geometry of the isotherms; raisingin areas with relatively warmer temperatures2. The lake bottom appears consistently warmer in thesouthern end of the lake, with two warm regions around latitudes of ∼ 49.945◦ and ∼ 49.967◦; thelayer depths mirror this variability by raising slightly above these two warm patches and having anoverall downward slope towards the northern end of the lake.A similar relationship between temperature distribution and layer slope was found in the two di-mensional laboratory study by Turner and Chen (1974), where it was shown that aside from bottomheating of a salt stratified fluid, layers could be set up in (at least) two other ways: by introducing aphysical slope to the system or by injecting water at one side with different temperature and salin-ity from (but same density as) the ambient fluid. Although seemingly very different approaches,the underlying mechanism leading to layer formation is identical: in both of these cases a horizon-tal gradient in temperature and salinity is established, and thus the iso-surfaces are not perfectlyhorizontal.Turner and Chen (1974) also showed that the established horizontal gradients drive convectionin the form of intrusion-like layers that propagate horizontally at a downward angle. After the2The correlation is not perfect since the horizontal within-layer variations in temperature (and salinity) are still non-zero (Figure 3.6)42Depth [m]2012−13 Survey Overlap330335340345350Depth [m]2013−14 Survey Overlap330335340345350Depth [m]Degrees Latitude [o]2014−15 Survey Overlap  49.94 49.95 49.96 49.97 49.98 49.99330335340345350Temperature [o C]9.269.279.289.299.39.319.329.339.349.359.36Figure 4.1: Outlines of overlapped DD layers from consecutive survey years, with 0.25 mvertically-binned background temperature in colour. Layers appear to be consistentlyraised in regions with relatively warmer waters. Note: 2015 data shifted downward by0.3 m to better align with 2014 data.43Figure 4.2: The circulation present within tilted layers. Adapted from Turner and Chen (1974).layers propagate to fill the entire domain, the overall appearance of the layers is nearly equivalentto those seen in the bottom heating case apart from one key feature: the layers formed in thisway are all sloped rather than aligned with the horizontal. Furthermore, the convection that drivesthe propagation of these layers is still persistent after they have filled the domain, so that there isan overall layer circulation such that the flow is downslope in the upper portion of the layer andupslope in lower portion of the layer (Figure 4.2).The effects of a physical slope, and thus the iso-surface slope, were shown by Chen and Liou(1997) to play an important role in the formation of layers, affecting their number, structure, andthickness. An investigation on the sidewall heating of a two-layer salt stratified system by Bergmanand Ungan (1988) indicated that the slope of the interface between the two layers was dependenton the applied horizontal temperature difference, suggesting that the slope of the DD layers wouldincrease with higher horizontal temperature gradients (given equal horizontal salinity gradients). Inboth studies the convective circulation observed within the layers was identical to that observed byTurner and Chen (1974). Weak horizontal circulation patterns were observed in naturally occurringDD staircase structures in the Arctic by Polyakov et al. (2012), and may indicate the possibility thatthe circulation patterns shown in Figure 4.2 may be present in geophysical settings as well.Thus, the angle of the layers is dependent upon the angle of the iso-surfaces of temperatureand salinity, and angled layers would result in a characteristic layer circulation. Since experimentsshow layers propagating downward and away from the site of heating (Turner and Chen, 1974),the formation sites of the layers can be identified as vertical peaks of the layer depths. This wouldimply that in Powell Lake the layers are maintained primarily from the south side of the lake, butalso around the two regions at latitudes of ∼ 49.945◦ and ∼ 49.967◦.This could possibly explain the layer present at a depth of 345 m which is consistently seento terminate at ∼ 49.958◦. If the horizontal gradients differ between the two warmer regions atlatitudes of∼ 49.945◦ and∼ 49.967◦, this would result in layers forming at those sites with different44properties. It is plausible that more layers could be formed in the warm region at∼ 49.945◦ than theone at ∼ 49.967◦. As the layers propagate outwards, the layers from each region would meet at thetrough of the isotherm contour at a latitude of∼ 49.958◦. However, because of the differing numberof layers formed at the two regions, a single layer would be left consistently unjoined. Mergingmight occur if the horizontal gradients were altered to be equal (but opposite in direction) at the twoformation sites, so that the number of layers formed at each site would be the same.In any layer where enough time has passed so that the system has stabilized to accommodate thehorizontal gradients, the temperature gradient would have an opposite sign to the salinity gradient(Turner and Chen, 1974). This would result in layers that appear warmer and less salty in raisedsections of the layer, and colder and more salty in lowered sections of the layers, such that the layerswould be most dense at their lowest point (and vice versa)3. These opposing gradients would implythat the the resulting value of Rρx would be negative, which was shown to be the case for layersoccurring in the Arctic (Timmermans et al., 2008), as well as in the present study of Powell Lake.Furthermore, since horizontal gradients would occur only for sloped layers (and vice versa), anon-zero value of Rρx would imply the existence of a sloped layer, with the magnitude possiblybeing related to the slope. Data of this sort is scarce, but a start is provided here showing that for avalue of Rρx =−0.35±0.17, the observed mean layer slope is ∆z/∆x= 0.05±0.02 m/km.4.4 Summary and Future WorkThe results of the present work indicate that the regime of Rρz > 2, with Ra ≈ 107, consists ofDD layers that are stable and do not merge, with a convective regime within the layers dominatedby intermittent, buoyancy driven thermal plumes. These results are consistent with findings fromnumerical and laboratory studies of double diffusive systems, and suggests that other results fromthese studies can be carried over into the naturally occurring oceanic cases of double diffusiveconvection.The horizontal coherence of the layers was consistent over the course of 4 years even whensubject to persistent seiche activity, thus reinforcing the stability of these structures. The mostcoherent layers were observed in the central region of the domain, with a value of Rρz = 2.2±0.2;the less coherent layers were found above and below the central region with Rρz values that weregreater than those found in the central region. Qualitative differences between the layers above andbelow the central region with similar values of Rρz but differing values of Ra implied that the mosthorizontally coherent layers would have the lowest (yet still stable) value of Rρz with the highest Ravalue, such that for two layers with equivalent values of Rρz, the layer with the higher Ra numberwould be more horizontally coherent.The layers showed consistent variability in the layer depths and background temperature overthe 4 years. The sloped sections of the layers appeared to be correlated with the presence of hori-zontal gradients of temperature and salinity, thus implying a relationship between Rρx and the layer3A subtlety present here is that the ‘horizontal’ gradients within the tilted DD layers would oppose one another, butthe background horizontal gradients would still point in the same direction.45slope. Based on laboratory and numerical work, it is probable that due to the existence of a slope ofthe layers present at Powell Lake, there is a very slow large-scale along-layer circulation that wouldbe occurring at the same time as the short scale convection due to the thermal plumes.The presence of horizontal gradients suggests an altered picture for how the layers are formedand maintained within the environment at Powell Lake. Instead of the classic situation arising fromfrom the case of the bottom heating of a salt stratified system – the development of a large initialconvective layer at the bottom with subsequent layers developing one at at a time above that – theprocess here may rely on a slightly altered mechanism.That is, due to the non-uniform temperature (and salinity) distribution at the lake bottom, it ispossible that the layers are formed/maintained via a method which combines the layer-upon-layerformation associated with bottom heating experiments, and the horizontal propagation of slantedintrusion-like layers associated with side heating experiments. This would imply that in addition tothe presence of a vertical heat flux, there would also be a (presumably small) horizontal heat fluxwhich would act to adjust non-uniformities in the near-bottom fluxes to a different distribution in theupper waters. Thus, the horizontal variability of the bottom temperature creates a situation wheretwo dimensional effects become visible, primarily in the existence of a layer slope.Testing this hypothesis for the layer up-keep mechanism at Powell Lake would require furtherstudy specifically including detailed profiling of the structure of the currents within the layers (whichare presumably much smaller than the ∼0.5 mm/s velocity of the plumes), alongside more detailedstudy of the variability of the layer depths, to more accurately describe their geometry. Also, therelationship between Rρx and the layer slope mights (in part) be determined from previous studiesof naturally occurring layers where horizontal coherence has been found (e.g. Padman and Dillon(1987), Timmermans et al. (2008), Polyakov et al. (2012)).Furthermore, laboratory and numerical studies could be performed on a bottom heated salt strat-ified fluid with a non-uniform bottom heat flux or bathymetry in order to better understand the re-lationship between the boundary heating conditions and the resultant layer geometry. Ideally, thecirculation would also be determined within such systems so that the layer geometry, circulation,and background temperature/salinity distributions could be linked together.46Chapter 5ConclusionsA study was performed in order to determine the spatial and temporal properties of naturally oc-curring double diffusive structures present at the bottom of Powell Lake. The aim of the study wasto characterize the processes occurring on the scale of the overall layered DD staircase structure aswell as within an individual DD layer. In order to achieve these aims, observations on the scaleof the whole staircase structure were made by means of four annual surveys of cm-vertical and∼300m-horizontal resolution CTD profiles along the 9 km length of the lake, and on the scale ofan individual step by means of a month-long mooring consisting of thirty-eight temperature sensorsand two current meters spaced vertically over 2 metres.Within an individual DD layer, plume-like features were observed to be generated intermittentlyat the lower diffusive interface. These features were observed to have a characteristic commonpeak in the power spectra of the mean temperature of the convective region and the horizontalcurrents. The period of this peak was found to be ∼ 22 minutes, which is near identical to theestimate of the buoyancy period of the diffusive interface within that region. It was concludedthat the convective regime within this DD layer is composed of intermittent thermal plumes for avertical density ratio of Rρz = 2.2±0.2, and Rayleigh number of Ra≈ 107. This is consistent withresults from numerical and laboratory studies that show that the convective regime is composed ofintermittent thermal plumes for the regime of Rρz > 2. The temperature scale for these plumes wasestimated to be T ′≈ 0.2 m◦C, with associated vertical and horizontal velocity scales of w′= u′≈ 0.5mm/s. Comparison with the mean vertical heat flux of 27mW/m2 indicated that the warm upward-going plumes cover ∼ 13% of the total area, so that the other ∼ 87% is dominated by weakerdownward-going colder flows.DD steps within individual CTD profiles were identified and combined with those from adjacentprofiles to form DD layers by means of isolating the clusters found on T-S diagrams, effectivelymatching up closest step salinity among adjacent profiles. The structure of the DD layers wasobserved to be consistent over the course of the entire study period and showed remarkable temporalpersistence, as the same∼ 20 layers were tracked throughout all for years of study. The layers in thecentral range (within depths of 336-347 m) were consistently horizontally-coherent over the entirelake length with near constant values of the vertical density ratio, Rρz = 2.2± 0.2, and buoyancy47frequency, N = (2.3±0.3)×10−3 s−1, along with a peak in the Rayleigh number, Ra≈ 107 . Thelayers above and below this region were observed to be less horizontally-coherent, with greatervalues of Rρz and N. The top layers were more coherent than those near the bottom, suggestingthat Rρz is not the only parameter that determines the horizontal coherence of DD layers, and thatgiven identical values of Rρz, layers with higher Ra are likely to be more horizontally coherent. Thelack of observed layer merging over time in the central region indicates that for Rρz = 2.2±0.2 andRa = 106− 107 the layers are in a (quasi-) stable state. In this regime, the convective state withinlayers is strong enough to maintain well defined and horizontally-coherent layers, but not strongenough to cause those layers to become unstable.The use of the closest profile-to-profile salinity as a criterion for isolating DD layer clusters on aT-S diagram indicated that the layers at Powell Lake tend to follow iso-surfaces of salinity. However,the depth variability of the layers also mimics the variability in the iso-surfaces of the backgroundtemperature, suggesting that layer depth is closely connected to the background temperature field.An implication of this is that DD layers are sloped in the presence of horizontal gradients of back-ground temperature and salinity, and that the horizontal density ratio, Rρx, of the layers would berelated to their mean slope, such that a non-zero value would indicate the presence of a sloped layer.It was shown that the temperature and salinity gradients along layers were persistent over the courseof the study. Layers had a tendency to be colder by 2 m◦C and saltier by 0.1 g/kg in the northernend, relative to the southern end of the lake. These layer gradients produce a horizontal density gra-dient of Rρx = −0.35± 0.17, and are accompanied by a mean layer slope of ∆z/∆x = 0.05± 0.02m/km. The fact that the layers are sloped and not perfectly horizontal would imply that there is acharacteristic horizontal circulation within the layers, as seen in side heating experiments. This cir-culation should have the effect of homogenizing the spatial variation in the heat flux, so that layersfurther away from the (non-uniform) heating boundary should be less variable in their structure.The results and suggestions presented in this study bring up several questions which lead tonovel directions for the course of further study within the field of double diffusive convection,mainly dealing with the geometry of the formed layers and their relationship to background fieldsof temperature and salinity. In the case of Powell Lake, further work could be done to attain moreprecise measurements of the structure of the background temperature, salinity, and velocity fields, inorder to determine precise relationships between those fields and the accompanying layer geometry.Previous field studies could also be revisited in order to determine if there is indeed a relationshipbetween mean layer slope and the value of Rρz. Finally, laboratory and numerical studies could beincorporated by revisiting the standard salt-stratified heating experiments, except with non-uniformbottom heating or topography conditions to determine their effects on the geometry of the resultingDD layers.48BibliographyBeckermann, C. and Viskanta, R. (1989). An experimental study of melting of binary mixtureswith double-diffusive convection in the liquid. Experimental Thermal and Fluid Science,2(1):17–26. → pages 8Bergman, T. L. and Ungan, A. (1988). A note on lateral heating in a double-diffusive system.Journal of Fluid Mechanics, 194:175–186. → pages 44Carmack, E. C., Williams, W. J., Zimmermann, S. L., and McLaughlin, F. a. (2012). The ArcticOcean warms from below. Geophysical Research Letters, 39(7):1–6. → pages 6, 40Carpenter, J. R., Sommer, T., and Wu¨est, a. (2012). Stability of a Double-Diffusive Interface in theDiffusive Convection Regime. Journal of Physical Oceanography, 42(5):840–854. → pages 8,37, 41Chen, Y.-M. and Liou, J.-K. (1997). Time-dependent double-diffusive convection due tosalt-stratified fluid layer with differential heating in an inclined cavity. International Journal ofHeat and Mass Transfer, 40(3):711–725. → pages 44Crapper, P. F. (1975). Measurements across a diffusive interface. Deep Sea Research, 22(August1975):537–545. → pages 4, 37Flanagan, J. D., Lefler, A. S., and Radko, T. (2013). Heat transport through diffusive interfaces.Geophysical Research Letters, 40(10):2466–2470. → pages 8, 37Hoare, R. a. (1968). Thermohaline convection in Lake Vanda, Antarctica. Journal of GeophysicalResearch, 73(2):607. → pages 6, 40Huppert, H. E. (1971). On the stability of a series of double-diffusive layers. Deep Sea Researchand Oceanographic Abstracts, 18(10):1005–1021. → pages 8, 38, 40Hyndman, R. D. (1976). Heat flow measurements in the inlets of southwestern British Columbia.Journal of Geophysical Research, 81(2):337–349. → pages 12, 13, 39IOC, SCOR, and IAPSO (2010). The international thermodynamic equation of seawater - 2010:Calculation and use of thermodynamic properties. Manual and Guides No. 56.Intergovernmental Oceanographic Commission, UNESCO (English). Available fromhttp://www.TEOS-10.org. → pages 13Kelley, D. E., Fernando, H. J. S., Gargett, a. E., Tanny, J., and O¨zsoy, E. (2003). The diffusiveregime of double-diffusive convection. Progress in Oceanography, 56(3-4):461–481. → pages2, 449Kunze, E. (2003). A review of oceanic salt-fingering theory. Progress in Oceanography,56(3-4):399–417. → pages 2Lavery, A. and Ross, T. (2007). Acoustic scattering from ocean microstructure. The Journal of theAcoustical Society of America, 87(S1):S6. → pages 5, 37Lawson, K., Lemieux, B., Luck, J., and Woody, D. (1983). The development of a spherical,electromagnetic current meter. pages 187–193. → pages 18Linden, P. F. and Shirtcliffe, T. G. L. (1978). The diffusive interface in double-diffusiveconvection. Journal of Fluid Mechanics, 87(03):417. → pages 8, 37Marmorino, G. O. and Caldwell, D. R. (1976). Heat and salt transport through a diffusivethermohaline interface. Deep Sea Research and Oceanographic Abstracts, 23(1):59–67. →pages 4, 5, 37, 39Mathews, W. H. (1962). Bathymetry of Powell Lake, British Columbia. Technical Report 13,Institute of Oceanography, University of British Columbia. → pages 11Mathews, W. H., Fyles, J., and Nasmith, H. (1970). Postglacial crustal movements in southwesternBritish Columbia and adjacent Washington State. Canadian Journal of Earth Sciences,7(2):690–702. → pages 11Nettelmann, N., Fortney, J. J., Moore, K., and Mankovich, C. (2015). An exploration of doublediffusive convection in Jupiter as a result of hydrogen-helium phase separation. Monthly Noticesof the Royal Astronomical Society, 447:3422–3441. → pages 8Newell, T. a. (1984). Characteristics of a double-diffusive interface at high density stability ratios.Journal of Fluid Mechanics, 149(-1):385. → pages 4, 5, 37, 40Noguchi, T. and Niino, H. (2010a). Multi-layered diffusive convection. Part 1. Spontaneous layerformation. Journal of Fluid Mechanics, 651:443. → pages 7Noguchi, T. and Niino, H. (2010b). Multi-layered diffusive convection. Part 2. Dynamics of layerevolution. Journal of Fluid Mechanics, 651:465. → pages 8Osborn, T. R. (1973). Temperature microstructure in Powell Lake. Journal of PhysicalOceanography, 3:302–307. → pages 12Padman, L. and Dillon, T. M. (1987). Vertical heat fluxes through the Beaufort Sea thermohalinestaircase. Journal of Geophysical Research: Oceans, 92(C10):10799–10806. → pages 6, 21, 38,46Perry, K. and Pedersen, T. (1993). Sulphur speciation and pyrite formation in meromicticex-fjords. Geochimica et cosmochimica acta, 57(18):4405–4418. → pages 12Polyakov, I., Pnyushkov, A., Rember, R., Ivanov, V., Lenn, Y., Padman, L., and Carmack, E.(2012). Mooring-based observations of double-diffusive staircases over the Laptev Sea slope.Journal of Physical Oceanography, 42(1):95–109. → pages 6, 21, 44, 46Qiu, X.-L., Shang, X.-D., Tong, P., and Xia, K.-Q. (2004). Velocity oscillations in turbulentRayleigh−Benard convection. Physics of Fluids, 16(2):412. → pages 3850Radko, T. (2003). A mechanism for layer formation in a double-diffusive fluid. Journal of FluidMechanics, 497(December 2003):365–380. → pages 8, 40Radko, T. (2013). Double-diffusive Convection. Cambridge University Press. → pages 2, 5Rosenblum, E., Garaud, P., Traxler, a., and Stellmach, S. (2011). Turbulent Mixing and LayerFormation in Double-Diffusive Convection: Three-Dimensional Numerical Simulations andTheory. The Astrophysical Journal, 731(1):66. → pages 8Ross, T. and Lavery, A. (2009). Laboratory observations of double-diffusive convection usinghigh-frequency broadband acoustics. Experiments in Fluids, 46(2):355–364. → pages 5, 37Ruddick, B. and Gargett, A. E. (2003). Oceanic double-infusion: Introduction. Progress inOceanography, 56(3-4):381–393. → pages 1Sanderson, B., Perry, K., and Pedersen, T. (1986). Vertical diffusion in meromictic Powell Lake,British Columbia. Journal of Geophysical Research, 91:7647–7655. → pages 11, 12Scheifele, B. (2013). Double diffusion in Powell Lake: New insights from a unique case study.Masters thesis, University of British Columbia. → pages 14, 16, 22Scheifele, B., Pawlowicz, R., Sommer, T., and Wuest, A. (2014). Double diffusion in saline PowellLake, British Columbia. Journal of Physical Oceanography, 44(2):2893–2908. → pages iii, v,7, 12, 13, 21, 39, 41Schmid, M., Busbridge, M., and Wu¨est, A. (2010). Double-diffusive convection in Lake Kivu.Limnology and Oceanography, 55:225–238. → pages 7, 21, 38Schmid, M., Lorke, A., Dinkel, C., Tanyileke, G., and Wu¨est, A. (2004). Double-diffusiveconvection in Lake Nyos, Cameroon. Deep-Sea Research Part I: Oceanographic ResearchPapers, 51(8):1097–1111. → pages 7Shirtcliffe, T. (1969). The development of layered thermosolutal convection. International Journalof Heat and Mass Transfer, 12(2):215–222. → pages 7Sirevaag, A. and Fer, I. (2012). Vertical heat transfer in the Arctic Ocean: The role ofdouble-diffusive mixing. Journal of Geophysical Research: Oceans, 117(7):1–16. → pages 6,40Sommer, T., Carpenter, J. R., Schmid, M., Lueck, R. G., Schurter, M., and Wu¨est, A. (2013).Interface structure and flux laws in a natural double-diffusive layering. Journal of GeophysicalResearch: Oceans, 118(11):6092–6106. → pages 7, 41Stern, M. E. (1960). The ”Salt-Fountain” and Thermohaline Convection. Tellus A, 1. → pages 1, 3Stern, M. E. (1969). Collective instability of salt fingers. Journal of Fluid Mechanics,null:209–218. → pages 8Timmermans, M.-L., Toole, J., Krishfield, R., and Winsor, P. (2008). Ice-Tethered Profilerobservations of the double-diffusive staircase in the Canada Basin. Journal of GeophysicalResearch, 113. → pages 6, 22, 23, 40, 41, 45, 4651Toffolon, M., Wu¨est, A., and Sommer, T. (2015). Minimal model for double diffusion and itsapplication to Kivu, Nyos, and Powell Lake. Journal of Geophysical Research: Oceans,120(9):6202–6224. → pages 7Turner, J. (1965). The coupled turbulent transports of salt and and heat across a sharp densityinterface. International Journal of Heat and Mass Transfer, 8(5):759–767. → pages 3, 4Turner, J. S. (1968). The behaviour of a stable salinity gradient heated from below. Journal ofFluid Mechanics, 33:183–200. → pages 3, 5, 37, 40Turner, J. S. and Chen, C. F. (1974). Two-dimensional effects in double-diffusive convection.Journal of Fluid Mechanics, 63:577–592. → pages iii, v, 5, 40, 42, 44, 45Veronis, G. (1965). On Finite Amplitude Instability in Thermohaline Convection. Journal ofMarine Research, 23(1):1–17. → pagesvon Rohden, C., Boehrer, B., and Ilmberger, J. (2010). Evidence for double diffusion in temperatemeromictic lakes. Hydrology and Earth System Sciences, 14(4):667–674. → pages 7Williams, P. M., Mathews, W. H., and Pickard, G. L. (1961). A lake in British Columbiacontaining old sea-water. Nature, 191:830–832. → pages 11Zhou, S. Q. and Lu, Y. Z. (2013). Characterization of double diffusive convection steps and heatbudget in the deep Arctic Ocean. Journal of Geophysical Research: Oceans,118(12):6672–6686. → pages 6, 38Zhou, S. Q., Qu, L., Lu, Y. Z., and Song, X. L. (2014). The instability of diffusive convection andits implication for the thermohaline staircases in the deep Arctic Ocean. Ocean Science,10(1):127–134. → pages 652

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