Subgrid Length-Scales for Large-Eddy Simulation of Stratified Turbulence
The influence of buoyancy on the length-scales for the dissipation rate of kinetic energy, and for momentum, heat and other scalar transport has to be known for subgrid-scale (SGS) models in a Large-Eddy Simulation (LES). For the inertial subrange, Lilly (1967) has shown that the grid spacing is the relevant length- scale for SGS effects. Deardorff (1980) proposed to reduce all the length-scales for stable stratification. Numerical and experimental data show, however, that the dissipation length-scale may strongly increase in stable layers with little shear. Also Lumley’s (1964) theory for the energy spectrum in a stratified fluid suggests such an increase. In this paper we apply analysis of previous algebraic second-order closure SGS-models, parameter studies with different length-scale models in LES, and analysis of direct simulations of sheared and unsheared stably stratified homogeneous turbulence. These analyses suggest that the limiting effect of stratification should only be applied to the length-scales of vertical eddy-diffusivities of heat and scalars but not to those of momentum and dissipation.
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