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UBC Theses and Dissertations

Turbulence, diffusion and the daytime mixed layer depth over a coastal city Steyn, Douw Gerbrand


The rate of dispersion of atmospheric pollutants and the volume of atmosphere available for the dilution of pollutants are examined in an unstable suburban atmosphere at a coastal location. Within the framework of the statistical theory of diffusion, it can be shown that the non-dimensional dispersion functions σ[ sub y]/σ [sub v]t and σ[ sub z]/σ [sub w]t can be determined by integration of the Eulerian spectral functions multiplied by appropriately scaled sampling functions. This scaling, which arises out of the Hay-Pasquill form for the Eulerian-Lagrangian transform and the use of a non-dimensional frequency, gives rise to a dispersion scaling time t[sub s] = z/σ[sub u] which is simply related to the Lagrangian integral time scale. Applying this analysis to turbulent velocity spectra measured over a selected suburban surface results in the following forms for the crosswind and vertical dispersion functions respectively. S[sub y](t*) = (1.0 + 0.16√t*)⁻¹ S[sub z](t*) = (1.0 + 1.21√t*)⁻¹ The spectra and integral turbulence statistics determined in this part of the study are shown to be in general agreement with those determined over much smoother surfaces. The volume of atmosphere available for the dilution of pollutants is controlled primarily by the mean wind speed and mixed-layer depth. This latter variable can be modelled on the basis of a simple thermodynamic analysis of the mixed layer processes. The currently available models have been generalized to include advection and subsidence. The effects of advection on the mixed-layer depth have been modelled by resetting the model equations in a Lagrangian frame, performing an approximate first integral in order to derive the spatial dependence of the model variables, and using these spatial forms to give a set of Eulerian equations. The effects of subsidence have been modelled by imposing a subsidence velocity on the top of the mixed layer as well as allowing subsidence-induced warming of the atmosphere above that layer. This subsidence is driven by atmospheric divergence at both synoptic- and meso-scales, the latter phenomenon being linked to thermally driven circulatory systems. The inclusion of these processes into the mixed-layer depth model allows its application to areas in which meso-scale phenomena may have a considerable effect on the diurnal behaviour of the mixed-layer depth. The model thus derived consists of a system of non-linear differential equations which may be numerically solved to elucidate the temporal behaviour of the mixed-layer depth. The boundary conditions necessary for such a solution were provided by measurements made in the unstable surface layer over a coastal city. The resultant mixed-layer depth behaviour is in general in good agreement with determinations of this depth made with an acoustic sounder, but can be a poor reflection of reality in the presence of synoptic-scale non-stationarities. The input requirements of the model are hourly values of surface sensible heat flux, mean wind speed and upwind distance to the surface giving rise to the advected heat flux (usually a coastline or urban-rural boundary), and estimates of the intensity of the capping inversion and horizontal divergence. The model is sensitive to all input variables, the degree of sensitivity being indicated by the dependence of the maximum mixed-layer depth on the measured boundary conditions.

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