Frequency gap for higher equatorial wave modes
= Frequency gap for higher equatorial wave modes
For fixed positive frequency and $n\geq1$, the <equatorial shallow-water dispersion relation> has real zonal <wavenumbers> only if
$$
\frac{\omega^2}{\beta c}\leq n+\frac12-\sqrt{n(n+1)}\quad\hbox{or}\quad \frac{\omega^2}{\beta c}\geq n+\frac12+\sqrt{n(n+1)}.
$$
Between these values the zonal roots are complex, giving an evanescent response rather than freely propagating modes.