Penetrative Convection for Rotating Boussinesq Flow in Tilted f-planes

In this paper, we have performed linear instability analysis of the penetrative convection for the Boussinesq flow on a tilted f -plane. We have discussed the onset of instability as stationary and oscillatory convection. For the stationary convection, it has been shown that the penetration of convection is hindered by the stability of the upper, less unstable layer. For the oscillatory convection, however, the conclusion is different. We have computed the penetrative convection for both prograde and retrograde waves. The result indicates that for the prograde wave, under certain circumstances, the penetrative convection in the upper layer can be more vigorous than that in the lower unstable layer. For the retrograde wave, on the other hand, the stability in the upper layer always has a negative effect on the penetrative convection. Our calculation on the tilted f -plane has reproduced many features, such as teleconvection and multilayer roll convection, previously discovered on the penetrative convection in the spherical geometry. The dependence of penetrative distance on the Ekman number, the Prandtl number, and the stability parameter has been analyzed.