The equatorial bulge, angular momentum and planetary wave motion

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