Direct numerical simulations of Couette flow with unstable stratifications

A series of direct numerical simulations of Couette flow with unstable stratification have been performed with a second-order finite difference code, optimized for a GPU cluster (AFiD GPU). Defining $ h $ as the channel height, shear Reynolds numbers up to $ Re_\tau=hu_\tau /\nu \approx 370$ have been achieved. Looking at the different mean temperatures and velocities of the datasets, it can be seen that, as expected, the convection and shear regimes compete with each other. For low $ Ra $, the statistics show a shear dominated flow field, whereas it becomes more difficult for the shear to dominate in the higher $ Ra $ regime. Studying the the Nusselt number ($ Nu $) as function of the $ Re $ number for different $ Ra $ numbers shows that for higher $ Ra $ the heat transfer first decreases with increasing shear before it increases strongly for higher mechanical driving. This unexpected non-monotonic change of $ Nu $ as a function of $ Re $ is due to a breakup of the large scale convection rolls formed by the buoyancy forces when moderate shear is applied. The large scale dynamics of pure thermal and pure mechanical driving can be observed in the extreme cases.