Research note / structural placeholder
QGSW potential-vorticity structure
Placeholder page for Hoda's quasi-geostrophic shallow-water derivations. Replace with the full derivation when ready.
State variables
The model tracks horizontal velocity, layer depth, relative vorticity, and potential vorticity. The organizing invariant is shallow-water potential vorticity.
\( q = \frac{\zeta + f}{H} \)
Scaling
The Rossby number expresses the ratio of advective to rotational time scales.
\( Ro = \frac{U}{f_0 L} \)
Spherical geometry
On the sphere, coordinate choices affect numerical conditioning, vorticity reconstruction, and streamfunction inversion.