Abstract
Based on averaging of the direct numerical simulation data obtained earlier, statistical moments are calculated in a turbulent patch arising after internal wave overturning in a flow with obstacle and stable stratification. Temporal evolution and spatial behavior of the turbulent-scalar-flux transport equation budget have been studied. A priori estimations of approximations for the pressure-scalar-gradient correlation and turbulent-diffusion processes in this equation have been carried out. The performed analysis is helpful to explore the turbulent patch in terms of statistical moments, and to verify closure hypotheses in turbulence models. It is shown that, in the global balance of the turbulent-scalar-flux equation, the mean-shear and buoyancy productions and the pressure-scalargradient correlation are roughly balanced, as for the shear Reynolds stress equation, and in contrast to the scalar variance and normal Reynolds stress equations. The algebraic turbulent-scalar-flux relations of the gradient diffusion type, as well as those derived in local-equilibrium and nonequilibrium assumptions are incorrect; therefore the use of the full turbulent-scalar-flux equation is justified.
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