qgpv
quasigeostrophic potential vorticity
Description
Real valued property with dimensions \((x,y,z)\) and units of \(1/s\).
Discussion
The quasigeostrophic potential vorticty (QGPV) is defined as,
\[\textrm{QGPV} \equiv \partial_x v - \partial_y u - f_0 \partial_z \eta_\textrm{e}\]where \(\eta_\textrm{e}\) is the linear approximation to the isopycnal displacement, and related to excess density with \(N^2 \eta_\textrm{e}= \frac{g}{\rho_0} \rho\).
This same quantity can be computed from a stream function \(\psi\) with,
\[\textrm{QGPV} = \nabla^2 \psi + \frac{d}{dz}\left( \frac{f^2}{N^2} \frac{d \psi}{dz} \right)\]The coefficients \(A_0\) are linearly related to the QGPV and the streamfunction such that,
\[\textrm{QGPV} = \mathcal{DFT}_x^{-1} \left[\mathcal{DFT}_y^{-1} \left[ \mathcal{F}^{-1} \left[ \textrm{QGPV}^{klj} A_0^{klj} \right] \right] \right].\]