  Rossby-Haurwitz (RH) waves are important explicit solutions of the
incompressible Euler equation on a two-dimensional rotating sphere. In this
paper, we prove the orbital stability of degree-2 RH waves, which confirms a
conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech.
Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with
the main challenge being to establish suitable variational characterizations
for the solutions under consideration. In this process, the set of
rearrangements of a fixed function plays a vital role. We also apply our
approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and
zonal flows with monotone absolute vorticity.
