Free Surface

The free surface is the air-sea interface treated as a movable boundary whose height eta evolves in response to the flow, rather than held rigid. Its slope sets the barotropic pressure gradient: a geostrophic surface current balances the Coriolis force against the gradient of g eta. Free-surface ocean models solve the fast external gravity-wave mode, with phase speed sqrt(g H) near 200 meters per second over a 4,000 m depth, usually with split-explicit or implicit time stepping for stability. Sea-surface-height anomalies of order 1 meter, measured by altimetry, reveal the geostrophic circulation and eddy field.