Budget of the Scalar Variance Equation in a Turbulent Patch Arising from Lee Wave Breaking

Based on averaged data of the direct numerical simulations, statistical moments are obtained in a turbulent patch arising after lee wave overturning in a flow with stable stratification and obstacle. Temporal evolution and spatial behavior of the scalar-variance transport equation budget have been studied. A priori estimations of algebraic approximations for scalar dissipation, scalar variance and turbulent-diffusion processes in the scalar-variance equation have been carried out. Such an analysis is helpful to explore the turbulent patch in terms of statistical moments, and to verify closure hypotheses in turbulence models. In the global balance of the scalar-variance equation, the compensation of production by dissipation and advection is shown, as for the turbulent kinetic energy equation. The ratio of turbulent time scales of the scalar and velocity fields varies from 0.2 to 2.2 within the wave breaking region, and the global value of this parameter is close to unity during the quasisteady period. The algebraic expression derived from the assumption of production and dissipation balance is incorrect leading to unphysical negative values, therefore the use of the full scalarvariance equation in the turbulent transport model is justified.

Keywords:
stable stratification, internal wave breaking, flow above obstacle, direct numerical simulation, scalar dissipation, scalar variance, turbulence models. 
УДК 532.517.4

Budget of the Scalar Variance Equation in a Turbulent Patch Arising from Lee Wave Breaking