Potential-vorticity gradients in a meridional two-layer current
= Potential-vorticity gradients in a meridional two-layer current
{title2=$\nabla_h\bar q_{1,2}=(\mp FV,\beta)$}
For $\bar\psi_1=Vx$ and $\bar\psi_2=0$, the <two-layer quasi-geostrophic potential vorticity> is $\bar q_1=f_0+\beta y-FVx$, $\bar q_2=f_0+\beta y+FVx$. A perturbation therefore feels both the northward gradient $\beta$ and opposite zonal gradients $\mp FV$. Dropping the zonal gradients removes the instability mechanism from the linearization.