The equatorial bulge, angular momentum and planetary wave motion

The impact of the equatorial bulge on the equatorial angular momentum of pl anetary flows is investigated by considering both the situation on earth an d on a spherical planet. First, a rigorous proof of the suggestion of Bell is given that both the standard nonlinear and linear primitive equations ca pture the impact of the bulge almost correctly, despite the fact that a sph erical earth is assumed in these equations. Linear eigenmodes of shallow wa ter 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-->infinity are not affected by the bulge. For finite H, however, there are both gravi tational and rotational modes with equatorial angular momentum which are af fected by the bulge. In contrast, there is only one mode with equatorial an gular momentum on the spherical planet. This mode is stationary.