Year: 2004
Type: article
Abstract: The spontaneous generation of inertia-gravity waves by balanced motion is investigated in the limit of small Rossby number ⑀ K 1. Particular (sheared disturbance) solutions of the three-dimensional Boussinesq equations are considered.For these solutions, there is a strict separation between balanced motion and inertia-gravity waves for large times.This makes it possible to estimate the amplitude of the inertia-gravity waves that are generated spontaneously from perfectly balanced initial conditions.It is shown analytically using exponential asymptotics, and confirmed numerically, that this amplitude is proportional to ⑀ Ϫ1/2 exp(Ϫ␣/⑀), with a constant ␣ Ͼ 0 and a proportionality constant that are given in closed form.This result demonstrates the inevitability of inertia-gravity wave generation and hence the nonexistence of an invariant slow manifold; it also exemplifies the remarkable, exponential, smallness of the wave generation for ⑀ K 1.The importance of the singularity structure of the balanced motion for complex values of time is emphasized, and some general implications of the results are discussed.
Authors: J. Vanneste, I. Yavneh
Language: English
Subfield: Oceanography
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2077539443