Pressure work in a steady cross-isobaric wind
= Pressure work in a steady cross-isobaric wind
{title2=$-\rho^{-1}\mathbf u\cdot\nabla_hp=r|\mathbf u|^2$}
Dot the steady linear-drag momentum equation with the velocity. The <Coriolis force does no work>, so pressure-gradient work balances frictional dissipation. In a strictly geostrophic flow the wind is along isobars and pressure work vanishes. Cross-isobar motion supplies the positive pressure work needed to maintain a dissipative equilibrium.