Cross-equatorial Geostrophic Adjustment

Abstract

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 linearize...