= Double Kelvin-wave adjustment at a depth step
{title2=$A_t+(c_+-c_-)A_x=2(c_+-c_-)\eta_0\delta(x)$}
A long disturbance trapped on a depth step is sometimes called a double <Kelvin wave>. With $H_+>H_-$, $f>0$ and $c_\pm=\sqrt{gH_\pm}$, cross-step <geostrophic balance> and the along-step acceleration yield the transport equation shown for a background height jump $\eta_0\operatorname{sgn}(x)$. Its zero-initial-amplitude solution is $A=\eta_0[\operatorname{sgn}(x)-\operatorname{sgn}(x-(c_+-c_-)t)]$. The adjusted region diverts cross-step <volume flux> along the step; the propagating front still carries flux. This outer approximation does not resolve fast adjustment at the fronts.
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