Inertia-gravity wave breaking in three dimensions. Part II: Convectively unstable waves

Abstract

The three-dimensional breakdown of a large-amplitude, convectively unstable inertia-gravity wave is examined numerically as a function of primary-wave frequency and amplitude. The results confirm that near-inertial waves break down preferentially via shear instability even when the primary wave is initially overturned. As in the convectively stable near-inertial regime, the spectrum of instability energy is approximately isotropic in azimuthal orientation. At intermediate frequencies, wave breakdown is triggered by a transverse shear instability in the region of overturning. This behavior, displaying a clear preference for instability with horizontal component of wavevector in the transverse direction, is different from the breakdown of convectively stable waves at intermediate frequency examined in Part I. As the primary-wave frequency is increased further, shear instabilities once again develop in the transverse direction, but they are modified by convective instability as the billows reach finite amplitude. The influence of transverse vertical shear becomes progressively weaker as the wave frequency approaches the buoyancy frequency. In this limit, transverse convection leads to wave collapse, and there is no preferred scale of instability.