= Pressure-coordinate thermal wind
{title2=$u_{\ln p}=RT_y/f,\quad v_{\ln p}=-RT_x/f$}
Combining <geostrophic balance>, $fu=-\Phi_y$, $fv=\Phi_x$, with <hydrostatic balance>, $\Phi_p=-RT/p$, and commuting the horizontal and vertical derivatives proves the displayed equations. Horizontal derivatives hold <pressure> fixed. This relates <vertical shear> to horizontal <temperature gradients> away from the equator; the derivation requires nonzero <Coriolis parameter> and the validity of <geostrophic balance>.
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