= Geostrophic thermal wind with separable buoyancy
{title2=$\bar u=-zA'(y)/f_0$}
For $b=A(y)+B(z)$, constant nonzero $f_0$, and zero basic velocity at $z=0$, <thermal-wind balance> gives
$$
\bar u=-\frac{zA'(y)}{f_0},\qquad \bar v=0.
$$
With full buoyancy represented by $f_0\bar\psi_z$, the constant-coefficient <three-dimensional quasi-geostrophic potential vorticity> is $\bar q=f_0+zA''/f_0+f_0B'/N^2$. The <reference-buoyancy convention in quasi-geostrophic potential vorticity> changes only the uniform reference contribution.
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