Shear driven purging of negatively buoyant fluid from trapezoidal depressions and cavities

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Experimental data and large eddy simulation results are analysed to investigate shear driven entrainment of a negatively buoyant fluid from trapezoidal depressions and cavities. This flow is of relevance to a number of environmentally significant applications including purging of saline pools in rivers and pollutant dispersion in cities and towns situated within topographic depressions. New scaling relations for the entrainment rate are developed based on physical arguments. Our scaling relations are shown to agree well with both experiments and numerical simulations of this flow in trapezoidal cavities with aspect ratios ranging between 7 and 17, entry beach angles between 8° and 33°, and an exit beach angle of 33°. For the numerical simulations, a sub-filter scale turbulence model is used that combines the dynamic mixed model of Zang et al. [“A dynamic mixed subgrid-scale model and its application to recirculating flows,” Phys. Fluids A 5, 3186 (1993)]10.1063/1.858675 with the dynamic localization procedure of Piomelli and Liu [“Large eddy simulation of rotating channel flows using a localized dynamic model,” Phys. Fluids 7, 839 (1995)]10.1063/1.868607 and a buoyancy correction similar to that proposed by Brown et al. [“Large-eddy simulation of stable atmospheric boundary-layers with a revised stochastic subgrid model,” Q. J. R. Meteorol. Soc. 120, 1485 (1994)]10.1002/qj.49712052004 based on data measured in the stable atmospheric boundary layer. Simulations run using this model give significantly closer agreement with the experimental data than simulations run using a version of the dynamic Smagorinsky model with similar modifications. Support for the physical arguments upon which the scaling relations are based is obtained through a statistical analysis of the turbulent flow fields generated by the numerical simulations.