= Geostrophic adjustment of a finite-width current
{title2=$\lambda=c/f$}
An initial current $U\mathbf1_{|y|<a}$ with flat surface has two oppositely signed <vortex sheets>. On an <f-plane>, its local final <geostrophic balance> has
$$
\frac{\eta_f}H=-\frac{U}{2c}\left(e^{-|y-a|/\lambda}-e^{-|y+a|/\lambda}\right),\qquad \lambda=\frac cf,\quad c^2=gH.
$$
The <Rossby deformation radius> controls the edge layers. The height is continuous and odd; the along-strip velocity is $-g\eta_f'/f$ and has the sheet jumps. Outgoing <inertia-gravity waves> carry the energy not retained in this balanced component.
Back to article page
