Large-Scale Hydrostatic Motions

Abstract

For many motions in both the ocean and the atmosphere, the horizontal scale far exceeds the vertical scale of the motion. For example, motions in the ocean occurring in the thermocline will have a vertical scale of a kilometer or less, while the horizontal scales might be of the order of hundreds of kilometers. Motions in the ocean induced by traveling meteorological systems will have such large scales. If the motion has such disparate scales in the vertical and horizontal, we can expect important influences on the dynamics. First of all, we would expect that the vertical velocity will be small compared with the horizontal velocity, since the motion consists of nearly flat trajectories. That in turn could mean that the vertical acceleration is small. Such dynamical consequences often allow simplifications to our treatment of the physics, and we are always looking for such simplifications so that we can make progress with more difficult problems; not just make life easier for ourselves.