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.

The classical theories of the western boundary currents, proposed in the first half of the 20th century, are extended to include cases of zonally elongated and meridionally narrow ocean basins. Results show for the first time that in basins that are sufficiently narrow meridionally, the equatorward wind-driven transport away from the western boundary is lower than that in meridionally wide basins. Our theoretical results are employed to explain the low transport in the East Australian Current.

Ekman's (1905) solution for how wind affects ocean surface currents is revisited and extended analytically for a piecewise-constant profile of vertical diffusion. This allows a comprehensive understanding of how the surface current deflection angle relative to the wind direction varies with the profile of vertical diffusion.