= Godfrey island rule
{c}
= Island rule
{synonym}
For an island in a constant-depth ocean with <Sverdrup balance>, choose a counterclockwise contour running from the island's southern tip east to the basin wall, north along that wall, west to the northern tip, and south along the island's western coast. If that contour avoids dissipative boundary layers, the <ocean transport streamfunction> on the island is
$$
\psi_I=-\frac H{f(y_N)-f(y_S)}\oint_C\mathbf W\cdot d\mathbf l.
$$
Here $\mathbf W$ is the wind acceleration appearing in the depth-averaged momentum equation. The basin-boundary streamfunction is zero. This integral fixes the otherwise undetermined constant on the island without requiring a friction law, as in https://doi.org/10.1080/03091928908208894[Godfrey's original island-circulation model].
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