Cross-equatorial Geostrophic Adjustment

Abstract

A geostrophic adjustment model is used to find out how water can cross the equator, and how far it can reach, while conserving its potential vorticity, in the context of geostrophic adjustment. A series of problems is considered; all but the last permit variation north?south only. The first problem discusses the equatorial version of the classic midlatitude adjustment problem of a one-layer, reduced gravity fluid in the Southern Hemisphere which is suddenly permitted to slump away from its initially uniform height distribution. Fluid which crosses the equator reaches farther northward than it began south of the equator. The configuration in which fluid reaches the farthest north requires fluid starting as far south as is possible subject to water actually crossing the equator. Particles move north a distance of at most 2.32 deformation radii. This problem is then extended in turn to a one-layer fluid occupying all space, whose depth changes abruptly from one value to another, and to the linearized problem which is fully tractable analytically. A second layer, with a rigid lid, is also discussed. In common with many adjustment problems in which wave radiation to infinity is prohibited, although one may seek a steady final state, such a state is not achieved in these problems. However, wherever possible it is shown that the long-time average of the time-dependent problem is the steady state solution already found. An extension is then made to include east?west variation and the effect of side walls. It is found that the one-dimensional solutions describe the fluid behavior for much longer than would be anticipated. In these adjustment problems, cross-equatorial flow occurs in two ways. First, particles cross the equator a short distance as in the one-dimensional problem, and are then advected some way eastward. Second, particles cross the equator in the western boundary layer, where dissipation act to change the sign of the potential vorticity and so permits long northward migration.