Abstract

A long-standing issue in geophysical fluid dynamics has been to quantify the coupling between the slow balanced motion, which dominates the large-scale dynamics, and the much faster inertia-gravity waves. Pioneering work by Lorenz in the mid-1980s introduced the idea of near-invariant slow manifolds to characterise the balanced part of the motion. More recent work has concentrated on mechanisms of spontaneous generation, whereby inertia-gravity waves are emitted by slowly evolving balanced flows. Such mechanisms demonstrate the fundamental limitations of the concept of slow manifold; they may also constitute significant sources of wave activity in the atmosphere and ocean. In this talk, I will consider spontaneous wave generation in the small-Rossby-number (rotation-dominated) regime. In this regime, there is a strict time-scale separation between balanced motion and inertia-gravity waves. As a result, slow manifolds can be constructed that are invariant to all orders on the Rossby number. This implies that wave generation is exponentially weak in the Rossby number and cannot be captured by standard power-series expansions. Exponential asymptotics techniques can however be used to describe the waves generated. I will discuss the application of these techniques to low-order models and to some idealised flows.