  In this article, we investigate the incompressible 2D Euler equations on a
rotating biaxial ellipsoid, which model the dynamics of the atmosphere of a
Jovian planet. We study the non-zonal Rossby-Haurwitz solutions of the Euler
equations on an ellipsoid, while previous works only considered the case of a
sphere. Our main results include: the existence and uniqueness of the
stationary Rossby-Haurwitz solutions; the construction of the traveling-wave
solutions; and the demonstration of the Lyapunov instability of both the
stationary and the traveling-wave solutions.
