Modeling nonequilibrium and history effects of homogeneous turbulence in a stably stratified medium

Abstract

Abstract Homogeneous turbulence decay in a stably stratified flow has two distinct characteristics. One is countergradient fluxes that are developed to keep the energy budget in equilibrium. Another is the formation of gravity waves that contribute to the velocity variance with little vertical mixing. The prediction of these characteristics are investigated using a hierarchy of turbulence models. They include second-order models as well as models that solve the transport equations for the turbulent kinetic energy, its dissipation rate, the temperature variance and its dissipation rate. In the latter class of models, the vertical heat flux is calculated either from an algebraic equation or from a transport equation. The algebraic equation is derived by invoking equilibrium and nonequilibrium turbulence assumption. Thus, modeling level and the relative importance of nonequilibrium and history effects in the predictions of countergradient fluxes and gravity waves could be assessed. The investigation reveals that countergradient heat flux can be predicted even when the equilibrium assumption is invoked. However, the formation of gravity waves can be predicted only when the history effects of the vertical heat flux are accounted for properly. The decay rate of the total energy is very much affected by two model constants in the temperature variance dissipation rate equation. On the other hand, the calculated frequency and amplitude of the gravity waves are influenced by the model constants in the heat flux equation.