The effect of Coriolis force on nonlinear convection in a porous medium

Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number. For T a ≪ 0 ( 1 ) , the rotational effect is not significant. For 0 ( 1 ) ≪ T a ≪ 0 ( R log R ) , the Nusselt number decreases with increasing T a for a given Rayleigh number R . The flow has always a finite number of modes, but with increasing T a in this region, the number of modes decreases. The functional dependence of the Nusselt number on R and T a is found to have discontinuities as the number of modes N * reduces to N * − 1 . For 0 ( R log R ) ≪ T a ≪ 0 ( R ) , the Nusselt number is proportional to R T a ( log R T a ) . The stabilizing effect of rotation is so strong that the optimal solution has left with only one horizontal mode. For T a = 0 ( R ) , the Nusselt number becomes 0 ( 1 ) and the convection is inhibited entirely by rotation for T a > 1 π 2 R .