High resolution 3D direct numerical simulation (DNS) of a model tropopause jet, with an underlying convectively unstable layer, is performed. We obtain quasi-equilibrium turbulent dataset, in which the budgets are nearly balanced. Vertical profiles of turbulence statistics and budgets are presented. Using this DNS dataset, we evaluate the performance of some popular models used in second-order closure of turbulence. To our knowledge, this is first time that such a study is conducted for turbulence under the combined influence of shear and convection. From this quasi-equilibrium dataset, we unambigously identify layers of countergradient momentum and heat fluxes which occur near regions of penetrative convection. These are also regions where conventional second-order closure models fail.

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