Abstract
The response of a semi-infinite ocean to a slowly travelling atmospheric perturbation crossing the coast provides a simple example of the breakdown of nearly geostrophic balance induced by a boundary. We examine this response in the linear shallow-water model at small Rossby number
$\varepsilon \ll 1$
. Using matched asymptotics, we show that a long Kelvin wave, with
$O(\varepsilon ^{-1})$
length scale and
$O(\varepsilon )$
amplitude relative to quasi-geostrophic response, is generated as the perturbation crosses the coast. Accounting for this Kelvin wave restores the conservation of mass that is violated in the quasi-geostrophic approximation.
Funder
Natural Environment Research Council
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics