= Linearized shallow-water potential-vorticity anomaly
{title2=$q=\zeta-f\eta/H$}
For a constant-depth resting layer on an <f-plane>, the depth-scaled linear <potential vorticity> anomaly is
$$
q=\zeta-\frac fH\eta,\qquad \zeta=v_x-u_y.
$$
It satisfies $q_t=0$ under the <linearized shallow water equations>. The physical perturbation of $(f+\zeta)/(H+\eta)$ is $q/H$. The signed scalar $q$, not its absolute value, is used in <potential-vorticity inversion> and balanced energy pairings.
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