= Energy retention in finite-width geostrophic adjustment
{title2=$E_b/E_i=(1-e^{-2r})/(2r)$}
For an initially uniform strip current of half-width $a$, the final balanced energy fraction is
$$
\frac{E_b}{E_i}=\frac{1-e^{-2r}}{2r},\qquad r=\frac a\lambda.
$$
The fraction tends to $1-r+O(r^2)$ for a narrow strip and to $1/(2r)$ for a wide strip. The difference is outgoing <inertia-gravity wave> energy, consistent with <conservation of energy>; the infinite-strip energies are interpreted per unit along-strip length.
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