The paper examines the applicability of known linear wave theories to numerical simulations of two, zonally invariant, fundamental problems of Physical Oceanography: Geostrophic adjustment and Ekman Adjustment. By simulating the problems with a modified version of the Massachusetts Institute of Technology General Circulation Model (MITgcm) we show that neither of the known wave theories can explain the results of the simulations in large and small meridional domains and for long and short times.

The work develops a Lagrangian theory of the transport on the continental shelf forced by periodically rotating wind driven. A strong resonance occurs when the wind stress rotates counterclockwise at the local Coriolis frequency, manifested in a fast longshore drift. For clockwise sub-inertial wind rotation the drift is directed with the coast to its right while in all other frequencies the drift is directed with the coast to its left.

The transition from an arbitrary initial sea surface height to a geostrophic balance in which the velocity is steady was solved last century for constant Coriolis frequency, f(y), where y is the latitude. This study extends the theory to the realistic case in which f(y) is linear with y. We find that the variation in f(y) translates the steady geostrophic state westward as low-frequency Rossby waves that are harmonic in narrow domains and trapped near the equatorward boundary in wide ones.