Second- and third-order moment budgets in a turbulent patch resulting from internal gravity wave breaking

Abstract

To study second- and third-order statistical moments in a quasi-steady turbulent region observed in stratified flows over obstacles after the wave breaking, the direct simulation method developed for variable density fields is used. The data of runs at Re = 4000, Fh = 0.6 (based on obstacle height and inflow velocity) are used to obtain time dependence and spatial distributions of Reynolds stress tensor components, turbulent kinetic energy, scalar variance, triple correlations, and terms of budgets of their transport equations. The analysis shows that the global balance for both scalar variance and turbulent kinetic energy is between mean-shear production, advection and dissipation, whereas locally buoyant production and turbulent transport due to third-order moments are significant. For normal Reynolds stresses, the pressure-strain term is important too, providing the redistribution of stress components. The studies allow us not only to explore the turbulent patch by means of statistical moments, but also to examine closure assumptions for separate items and evaluate geophysically interesting quantities produced from the averaged data.