Interaction between thermal convection and mean flow in a rotating system with a tilted axis

Abstract

Thermal convection in a sine-type horizontal shear flow in a rotating system with the rotation axis tilted from the vertical direction is investigated, sweeping three parameters: Taylor number, tilt angle of the rotation axis (i.e. latitude) and Rayleigh number. Nonlinear time evolutions show that there is not only a regime in which roll convections of a herringbone pattern accelerate a mean flow but also a regime in which a large-scale east–west roll convection accelerates the mean flow strongly. The parameter region in which this type of stable steady two-dimensional (2D) roll solution exists is determined by linear stability analyses. Even when the 2D steady solution is not linearly stable, unsteady quasi-periodic solutions oscillating around the steady solution can be found in the nonlinear time evolutions. Finally, a simple mechanism for the acceleration of the mean flow by the large-scale east–west roll convection is described in detail, in which both the tilt of the rotation axis and the sine-type horizontal shear of the flow are important.