= Kelvin-wave coastal amplitude scaling
{c}
{title2=$A_0\propto\sqrt{|f|/H}$}
For a harmonic coastal <Kelvin wave>, $v=(c/H)\eta$, $c=\sqrt{gH}$ and the offshore decay length is $c/|f|$. Integrating the period-mean pressure-work flux over the offshore direction gives $\mathcal F=\rho g^2 H A_0^2/(4|f|)$ for peak coastal amplitude $A_0$. Slow changes with negligible dissipation or scattering conserve this flux, giving $A_0\propto\sqrt{|f|/H}$. The changing mode width explains why depth scaling differs from fixed-width wave shoaling. The approximation is not uniform at the equator.
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