= Rossby-wave isofrequency circle
{c}
{title2=$\left(k+\beta/(2\omega)\right)^2+l^2=\beta^2/(4\omega^2)-a^2$}
The <wavevectors> of a nonzero-frequency <Rossby wave> in a resting shallow layer satisfy
$$
\left(k+\frac\beta{2\omega}\right)^2+l^2=\frac{\beta^2}{4\omega^2}-a^2.
$$
This follows by completing the square in the <shallow-water Rossby-wave dispersion relation>. A real circle requires $|\omega|\leq|\beta|/(2|a|)$. Its two intersections with a given tangential wavenumber provide the incident and reflected normal wavenumbers at a meridional wall.
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