Shallow-water quasi-geostrophic potential vorticity
= Shallow-water quasi-geostrophic potential vorticity
{title2=$Q=\nabla^2\psi-\psi/L_D^2+\beta y$}
For small Rossby number and small free-surface displacement, shallow-water potential vorticity reduces, up to a constant factor and additive constant, to relative vorticity plus background PV gradients and the stretching term $-\psi/L_D^2$.