Appendix A: The governing equations
 (1) (2)

The governing equations are non-dimensionalized using the thickness of layer d as length scale, thermal diffusion time as time scale, as velocity scale, and as temperature scale. is the thermal diffusivity and is the absolute value of temperature gradient of the basic state determined by the heat flux at the boundaries. are stream function and temperature disturbance, respectively. is the two-dimensional Laplacian operator, and is the Jacobian. Non-dimensional numbers appearing in the system are the Rayleigh number , the Prandtl number , and the parameter of topographic b effect , where is the thermal expansion coefficient, g is the gravitational acceleration, is the kinematic viscosity, is inclination of the boundaries, l is the size in the direction of the rotation axis, and E is the Ekman number .

 Appendix A: The governing equations