= Potential-vorticity inversion
Potential-vorticity inversion recovers a balanced <velocity field> from <potential vorticity> and specified boundary and global data. In <two-dimensional vortex dynamics> this is a <Poisson equation>; <shallow-water quasi-geostrophic inversion> and <stratified quasi-geostrophic inversion> use different <elliptic boundary value problems>. Advance the materially conserved scalar, then invert again to recover the evolving flow. Boundary <buoyancy> can induce flow with zero interior anomaly. The balance relation and <boundary conditions> are essential: unrestricted <gravity waves> are additional degrees of freedom. https://pordlabs.ucsd.edu/wryoung/theorySeminar/pdf14/McIntyrePV.pdf[McIntyre's potential-vorticity account] explains the general invertibility principle.
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