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.

Mean surface transport forced by wind blowing over an ocean can assume many directions relative to the wind direction and does not have to be perpendicular to the direction of the wind. This is in contrast to a simpler 120-year-old theory that completely ignored Earth's sphericity and predicted that the mean ocean current should always be perpendicular to the direction of the overlying wind. In the new theory the direction of the mean current is determined by the values of several parameters.

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.