The non-dimensional governing equations are those of a two-dimensional Boussinesq fluid with the topographic

beffect caused by the inclined boundaries (Busse,1986).

(1) (2)

yandqare stream function and temperature disturbance. Non-dimensional numbers appearing in the system are the Rayleigh number, the Prandtl numberR, and the parameter of topographicPbeffecth. Further explanation of these equations is given in Appendix A.The fixed heat flux condition is given as the thermal boundary condition.

(3) The kinematic and dynamic boundary conditions are impermeable and free-slip.

(4)