Abstract
The onset of thermal convection has been investigated numerically in turbulent shear flows, i.e. plane Couette and plane Poiseuille turbulence, between two horizontal plates heated from below. For fixed Reynolds numbers (Re = 750 for Couette flow; Re = 3000,4000,5000 for Poiseuille flow), the bulk Richardson number Ri is gradually increased to inspect the effects of buoyancy on shear-driven and pressure-driven turbulent flows. In plane Couette turbulence, buoyancy-induced streamwise rolls are observed to appear around Ri = 0.003, and they are found to be deformed into streamwise-dependent wavy rolls around Ri = 0.0071. At the higher Richardson number Ri 0.05 the wavy rolls propagate in the streamwise direction. In plane Poiseuille turbulence, buoyancy-induced streamwise rolls also appear at a certain value of Ri which depends on Re. The thermal convection in Poiseuille turbulence exhibits distinct bistable states: one is represented by the narrower rolls (1.2 times channel height) in the spanwise direction, and the other is represented by the much wider rolls (2.3 times channel height).
