We investigate the pressure torque between the fluid core and the solid mantle arising from magnetohydrodynamic modes in a rapidly rotating planetary core. A two-dimensional reduced model of the core fluid dynamics is developed to account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the assumption of invariance of the equatorial components of the fluid velocity along the rotation axis. We use this model to investigate and quantify the axial torques of linear modes, focusing on the torsional Alfven modes (TM) in an ellipsoid. We verify that the periods of these modes do not depend on the rotation frequency. Furthermore, they possess angular momentum resulting in a net pressure torque acting on the mantle. This torque scales linearly with the equatorial ellipticity. We estimate that for the TM calculated here topographic coupling to the mantle is too weak to account for the variations in the Earths length-of-day.
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