= Local Rossby-wave dispersion relation in a zonal jet
{title2=$\omega=kU-\frac{k(\beta-U^{\prime\prime}+U/R_D^2)}{k^2+l^2+R_D^{-2}}$}
When a zonal current varies slowly compared with the wavelength, freeze its velocity and background <potential vorticity> gradient locally in the <Rossby-wave equation for a sheared zonal current>. The resulting local <dispersion relation> includes curvature $U^{\prime\prime}$ and, for a free surface, the basic surface-slope contribution $U/R_D^2$. In the nondivergent limit it becomes $\omega=kU-k(\beta-U^{\prime\prime})/(k^2+l^2)$.
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