### Shallow Water QG

1. Use physical scaling arguments to derive the shallow water quasigeostrophic equations. Assume a $$\beta$$-plane.
2. Linearize this equation about a state of rest, assume a wave solution, and derive a dispersion relation for the Rossby waves on a $$\beta$$-plane
3. Determine the phase and group velocities for the waves.
4. Show that the meridional flux of zonal momentum $$\overline{u’v’}$$ is in the opposite direction of the meridional group velocity of the waves.

From Wikipedia.