Abstract
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 quasigeostrophic dynamics, and the rectangular basin geometry often used for theoretical studies of the wind-driven ocean circulation is such a singular case for quasigeostrophic 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 that 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 but closed along the equator yield basin modes sufficiently weakly damped that they could be resonantly excited.
Highlights
In recent articles, LaCasce (2000) and Cessi and Primeau (2001) have demonstrated that there exists, in the physically relevant case of weak friction, a set of weakly damped low-frequency basin modes
The basin modes consist of a westward propagating long Rossby wave excited by boundary pressure fluctuations at the eastern boundary and a uniform pressure adjustment that enforces mass conservation in the basin
It oscillates in time synchronously at all points along boundary despite the fact that the model formulation has a finite Kelvin wave propagation speed. This is not surprising since the time for a gravity wave to propagate around the boundary (26 days) is much shorter than the period of the mode (566 days). This suggests that free Kelvin waves are not the means by which the energy fluxed onto the western boundary by the long Rossby wave is returned to the eastern boundary
Summary
In recent articles, LaCasce (2000) and Cessi and Primeau (2001) have demonstrated that there exists, in the physically relevant case of weak friction, a set of weakly damped low-frequency basin modes. The basin modes consist of a westward propagating long Rossby wave excited by boundary pressure fluctuations at the eastern boundary and a uniform pressure adjustment that enforces mass conservation in the basin This uniform pressure adjustment is determined by imposing an integral constraint for mass conservation in the basin. For quasigeostrophic (QG) dynamics in a square basin the crossing time, given by the width of the basin divided by the long Rossby wave phase speed, is independent of latitude. Real ocean basins have large north–south extent so that the speed of long Rossby waves propagating in them depends on latitude contrary to the quasigeostrophic approximation. We will investigate the role played by the basin shape in both a quasigeostrophic setting and in a shallow water setting
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