= Rossby-wave PV mixing and zonal momentum
{c}
{title2=$\partial_t\overline U=\overline{v'q'}=-\partial_y\overline{u'v'}$}
In zonally averaged barotropic <quasi-geostrophic approximation> flow with zero mean meridional transport, the <Taylor identity for quasi-geostrophic flux> relates the meridional <potential vorticity> flux to the convergence of <Reynolds stress>. A local downgradient closure $\overline{v'q'}=-\kappa\overline Q_y$, with $\kappa\ge0$, therefore gives westward mean acceleration where the background gradient is positive. <Rossby wave> breaking can stir PV into fine filaments; coarse-graining or weak diffusion produces the inferred mixing. Globally the momentum-flux convergence integrates to boundary stresses, so localized westward changes need compensating transport or momentum changes elsewhere in an isolated system.
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