Cullen M.J.P. A Mathematical Theory of Large-scale Atmosphere/Ocean Flow

London: Imperial College Press, 2006. — 259 p.This volume is concerned with large-scale atmosphere/ocean flows. The traditional approximations used to describe such flows are based on smallness of the Rossby number, which states that large-scale flows are rotationdominated, the Froude number, which states that the flow is strongly stratified, and the aspect ratio, which states that the atmosphere is much shallower than the horizontal scale of most weather systems. These lead to the geostrophic approximation, which relates the horizontal wind to the horizontal pressure gradient. The semi-geostrophic equations developed by Hoskins, following earlier work by Eliassen, give a set of simplified equations which is valid on large scales. Their asymptotic validity requires a Lagrangian form of the Rossby number to be small, which means that fluid trajectories cannot curve too sharply. This is appropriate for extra-tropical weather system, including fronts and jet streams which are characterised by a large length-scale in one direction. They are not appropriate for smallerscale phenomena such as tropical cyclones, which are in a different asymptotic regime.