UBC Theses and Dissertations
The propagation of the internal tide around a bend in Knight Inlet, B.C. Webb, Anthony James
This thesis seeks to answer the question "how much of the internal tide propagating up Knight Inlet, B.C. is reflected by a right-angled bend ?" The internal tide in Knight Inlet is generated by the interaction of the barotropic tide with a shallow sill seaward of the bend. It then propagates in both directions as a travelling Kelvin wave. The up-inlet propagating wave then encounters the bend, where some of it may be reflected. This question is looked at with both theory (Chapter 2) and observations (Chapter 3). The theoretical study investigates the propagation of a Kelvin wave around a bend in a channel. The solution of the linearised long wave equations is expressed as a truncated series of cross-channel modes in each of three regions. The solution is matched across the two common boundaries by a least squares point matching process. The "rectangular bend" gives unsatisfactory results because of a singularity in the velocity field at the sharp inside corner. However, the "annular bend" gives good results. The bend acts as a diffraction grating, with total transmission for certain bend angles and "lobes" of high reflection for intermediate angles. Bends to the left give rise to the same reflection as bends to the right of the same angle, even if the incident Kelvin wave has a small cross-channel decay scale. For the parameters corresponding to the M₂ internal tide in Knight Inlet, the energy flux reflection coefficient is very small, much less than 1%. The method of solution breaks down inexplicably for diurnal tides. The observational study is based upon 2⅓ months of cyclesonde current meter data from four stations in Knight Inlet taken during the summers of 1981 and 1983. The vertical profiles of amplitude and phase of the M₂ constituent of longitudinal velocity and density fluctuations are found to be the same from month to month at a particular station, but different from station to station. These complex amplitude profiles are decomposed into a truncated series of normal modes for waves propagating both up-inlet and down-inlet. The phase speeds and zero-crossing depths of the normal modes do not agree with those calculated by Farmer and Smith (1980a) using 1977 data. Two simple models of the stratification are used to explain the differences in the normal modes in terms of differences in the Brunt-Väisälä frequency profile used to calculate them. At the two stations up-inlet of the sill, acceptable fits can be obtained using only two up-inlet propagating waves, indicating that the data are compatible with the low reflection found in the theoretical study. When down-inlet waves are included in the fit, their amplitudes are found to be small, although care must be taken to avoid trying to fit too many modes since some of them are highly correlated in the depth range for which data are available. At the two stations seaward of the sill, the up-inlet energy flux is of the same order of magnitude as the down-inlet flux, indicating a second source of internal tide seaward of those two stations. The results indicate that only 30-50% of the power removed from the barotropic tide is being fed into the internal tide in the summer. This conclusion is at variance with that of Stacey (1985), whose model shows that most of the power lost from the barotropic tide is being fed into the internal tide. A consistent interpretation of these results is that most of the power lost from the barotropic tide initially goes into the internal tide, but that 50-70% of it is rapidly dissipated through turbulence within a couple of kilometers of the sill. The low frequency component of the velocity signals from the cyclesonde data is also presented (Chapter 4), with a brief analysis . The monthly averaged residual velocity profiles are also found to be fairly repeatable from month to month at a particular station, but different from station to station. These profiles could be useful in validating general circulation models.
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