 Two-layer Sverdrup interior

For a uniform normalized upper-layer wind stress curl $W$ and no lower-layer forcing, a uniform local Sverdrup balance isThe upper layer flows meridionally and the lower layer rests. Although the relative vorticity vanishes, the potential vorticity has the zonal gradients ${\bar{q}}_{1,x}=-FV$, ${\bar{q}}_{2,x}=FV$. These are essential for the perturbation stability and do not vanish merely because the background velocity is uniform.