The equatorial bulge, angular momentum and planetary wave motion

Abstract

The impact of the equatorial bulge on the equatorial angular momentum of planetary flows isinvestigated by considering both the situation on earth and on a spherical planet. First, arigorous proof of the suggestion of Bell is given that both the standard nonlinear and linearprimitive equations capture the impact of the bulge almost correctly, despite the fact that aspherical earth is assumed in these equations. Linear eigenmodes of shallow water flow withequivalent depth H are discussed both for the spheroid with a corresponding torque and aspherical planet without torque. Surprisingly, it is found that Rossby–Haurwitz waves as rotationalmodes for H→∞ are not affected by the bulge. For finite H, however, there are bothgravitational and rotational modes with equatorial angular momentum which are affected bythe bulge. In contrast, there is only one mode with equatorial angular momentum on thespherical planet. This mode is stationary.