A finite volume dynamic large-eddy simulation method for buoyancy driven turbulent geophysical flows

A large-eddy simulation method based upon the finite volume approach is developed and evaluated for buoyancy driven turbulence in the absence of rotational effects. The effect of the sub-grid scale motions is modelled by using the dynamic scaling formulation, without introducing any ad hoc assumption for the vertical stratification. This way, the eddy coefficients for momentum and temperature equations are independently computed, while avoiding to introduce unjustified buoyancy production terms in the constitutive equations. As a result, the computational cost is considerably reduced with respect to the classical stratification formulation. The method is presented in detail, by stressing the particular features of the finite volume large-eddy simulation approach. The resulting numerical code is validated against a direct numerical simulation. Numerical experiments are conducted by simulating the thermal buoyancy driven turbulence near the water surface generated in a finite-depth stably stratified horizontal layer with an isothermal bottom surface. Diagnostics include time evolution of kinetic and thermal energy as well as energy spectral distribution. Interesting results are obtained by making a comparison with a reference spectral solution. The method is further validated for a turbulent ocean test case, that is the deepening of the mixed layer in a stable stratified fluid.