The three-dimensional breakdown of a large-amplitude, convectively stable inertia–gravity wave is examined numerically as a function of primary-wave frequency and amplitude. The results confirm that inertia–gravity waves in this region of parameter space break down preferentially via shear instability. In low-frequency waves the instability is ubiquitous, occurring simultaneously throughout the wave field, and the spectrum of instability energy is approximately, but not exactly, isotropic in azimuthal orientation. In higher-frequency waves, shear instability develops adjacent to the region of reduced static stability, and displays a preference for intermediate azimuths (e.g., near 45°). Near-inertial waves experience the fastest growing instabilities. The growth rate of shear instability drops off rapidly as the wave frequency is increased and, for all frequencies, increases with increasing wave amplitude. At most frequencies, the onset of modal shear instability occurs at a wave amplitude slightly above the theoretical stability boundary determined from a local Richardson number argument.
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Lelong et al. (1998) studied this question.