## Abstract

The spontaneous generation of inertia-gravity waves by balanced motion is investigated in the limit of small Rossby number kappa much less than 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 epsilon(-1/2) exp(-alpha/ epsilon), with a constant a. 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 e 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.

Original language | English |
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Pages (from-to) | 211-223 |

Number of pages | 13 |

Journal | Journal of the Atmospheric Sciences |

Volume | 61 |

Issue number | 2 |

Publication status | Published - Jan 2004 |

## Keywords

- ROTATING SHALLOW-WATER
- TAYLOR-COUETTE FLOW
- SLOW MANIFOLD
- INSTABILITY
- QUASIMANIFOLD
- DYNAMICS
- INITIALIZATION
- GEOMETRY
- MODEL
- SETS