Long Rossby wave basin-crossing time and the resonance of low-frequency basin modes

We demonstrate that the ability of long-wave low-frequency basin modes to be resonantly excited depends on the efficiency with which energy fluxed onto the western boundary can be transmitted back to the eastern boundary. This efficiency is greatly reduced for basins in which the long Rossby wave basin-crossing time is latitude dependent.

In the singular case where the basin-crossing time is independent of latitude the amplitude of resonantly excited long-wave basin modes grows without bound except for the effects of friction. The speed of long Rossby waves is independent of latitude for quasi-geostrophic dynamics, and the rectangular basin geometry often used for theoretical studies of the wind-driven ocean circulation is such a singular case for quasi-geostrophic dynamics.

For more realistic basin geometries, where only a fraction of the energy incident on the western boundary can be transmitted back to the eastern boundary, the modes have a finite decay rate which in the limit of weak friction is independent of the choice of frictional parameters. Explicit eigenmode computations for a basin geometry similar to the North Pacific show that the decay rates obtained in the physically relavent limit of weak friction are sufficiently small to allow the gravest modes to be resonantly excited. Spectral peaks at the modes resonant frequencies should be detectable in sufficiently long time series of thermocline displacements.