= Two-layer quasi-geostrophic potential vorticity
{title2=$F=k_I^2$}
For equal-depth layers coupled by an interface,
$$
q_1=f+\nabla_h^2\psi_1-F(\psi_1-\psi_2),\qquad q_2=f+\nabla_h^2\psi_2-F(\psi_2-\psi_1),\qquad F=k_I^2.
$$
The <Laplacian> terms are relative <vorticity>; the streamfunction differences encode opposite layer-thickness changes. Each <material derivative> follows that layer's own velocity. The sum has a <barotropic mode> without interface displacement, while the difference contains a <baroclinic mode>.
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