Effects of fluid properties on sheared thermal convection

A series of direct numerical simulations of sheared thermal convection have been performed with a second-order finite difference code (van der Poel et al., Comp. & Fluids, 116:10-16, 2015), optimized for a GPU cluster (AFiD GPU (Zhu et al., Comp. Phys. Comm., 229:199-210, 2018)), with a Rayleigh number Ra = 1x10⁶ and a wall Reynolds number Re_w of 0 ≤ Re_w ≤ 4000. We study the Prandtl number (Pr) dependency of flow structures in the regime of 0.22 ≤ Pr ≤ 4.6. Our findings show that a high Pr results in an increased dependency of Nusselt number and Re_w. At Pr = 4.6 we find a dependency of Nu(Re_w) ∝ 1x10^-3 Re_w in the shear dominated regime, while in the same regime for Pr = 0.22 and Pr = 0.46, Nu(Re_w) seems to collapse at Nu(Re_w) ∝ 1x10^-4 Re_w.

Additionally, we study the bulk Richardson number Ri_b - the ratio of buoyancy to mechanical forcing. For low Ri_b the flow settles in a regime dominated by the flow shearing, while a thermally dominated regime is present for high Ri_b. Various flow statistics have been plotted as a function of Ri_b^-1 to determine whether the Richardson number is a good estimator of the flow behavior. We show that in the studied parameter space Ri_b^-1 Ra^0.31 predicts Nu within 10%.