The paper examines the applicability of known linear wave theories to numerical simulations of two zonally invariant fundamental problems in Oceanography: The Geostrophic adjustment problem and the Ekman Adjustment problem. By simulating the problems with MITgcm we show that neither of the available wave theories is applicable to the explanation of the numerical results that are derived for large and small meridional domains.

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.