Balanced Atmosphere-Ocean Dynamics, Generalized Lighthill Radiation, and the Slow Quasi-Manifold

Abstract

Three of Lighthill's many interests, (a) wave propagation in moving media, (b) acoustic streaming and related phenomena, and (c), in a very subtle and fascinating way, aerodynamic sound generation, are all turning out to be fundamental to understanding our atmospheric environment. Among other things there is the global-scale circulation that shapes the ozone layer and controls the rate of destruction of man-made chlorofluorocarbons (CFCs). Recent progress in this field is sketched, including progress in understanding the abstract structure of Hamiltonian theories of balanced motion, the so-called slow “manifold”. Here a generic phenomenon, “velocity splitting”, turns out to be intimately related to aerodynamic sound generation, particularly its generalization describing the spontaneous emission of inertia–gravity waves from unsteady vortical motions in stratified rotating flow.