= Taylor identity for quasi-geostrophic flux
{c}
{title2=$\overline{v'Q'}=F_y+G_z$}
For zonal averages, $u'=-\psi'_y$, $v'=\psi'_x$, and $Q'=\nabla_H^2\psi'+\partial_z(S\psi'_z)$, with $S=f_0^2/N^2$ depending only on height, define $F=-\overline{u'v'}$ and $G=S\overline{\psi'_x\psi'_z}$. Integrating zonal derivatives by parts gives $\overline{v'Q'}=\partial_y\overline{\psi'_x\psi'_y}+\partial_z(S\overline{\psi'_x\psi'_z})$. This identity is exact within <quasi-geostrophic potential vorticity>, without assuming small disturbance amplitudes. Periodicity or appropriate vanishing zonal boundary terms is essential.
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