A three-dimensional and time-dependent numerical model is used to study the nonlinear interactions between thermal convective motions, rotation, and imposed flows with vertical shear. All cases have Rayleigh numbers of 104 and Prandtl numbers of 1.0. Rotating cases have Taylor numbers of 104.
For the non-rotating cases, the effects of the shear on the convection produce longitudinal rolls aligned with the shear flow and a downgradient flux of momentum. The interaction between the convection and the shear flow decreases the shear in the interior of the fluid layer while adding kinetic energy to the convective motions. For unit Prandtl number the dimensionless flux of momentum is equal to the dimensionless flux of heat.
For rotating cases with vertical rotation vectors, the shear flow favours rolls aligned with the shear and produces a downgradient flux of momentum. However, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. As in the non-rotating cases, the convective motions become more energetic by extracting energy from the mean flow. For Richardson numbers larger than about − 1.0, the dominant source of eddy kinetic energy is the shear flow rather than buoyancy.
For rotating cases with tilted rotation vectors the results depend upon the direction of the shear. For weak shear, convective rolls aligned with the rotation vector are favoured. When the shear flow is directed to the east along the top, the rolls become broader and the convection weaker. For large shear in this direction, the convective motions are quenched by the competition between the shear flow and the tilted rotation vector. When the shear flow is directed to the west along the top, strong shear produces rolls aligned with the shear. The heat and momentum fluxes become large and can exceed those found in the absence of a tilted rotation vector. Countergradient fluxes of momentum can also be produced.