Gravity wave breaking in two and three dimensions: 3. Vortex breakdown and transition to isotropy

Abstract

Companion papers by Andreassen et al. (this issue) and Fritts et al. (this issue) introduced a nonlinear, compressible, spectral collocation code and applied it to studies of gravity wave breaking in two and three dimensions. The former showed the two simulations to differ dramatically in the mode of instability and in its implications for the wave and mean flow evolutions. The latter considered in detail the structure and energetics of the instability and its influences via eddy transports of momentum and heat. This paper addresses the instability structure and evolution at late times, focusing specifically on secondary instability, vortex breakdown, and the transition to isotropic structure. These results exhibit several distinct behaviors, depending on the local environment. In the presence of weak environmental shears, vortex breakdown occurs through mutual interactions which cause a gradual nonlinear evolution toward smaller scales of motion. Where wave and mean shears are strong, vortex breakdown is accelerated by dynamical instability processes at small scales which modulate strongly the vortex structures due to wave instability. Spectral results suggest that our simulation has described the transition from two‐dimensional laminar wave motions to three‐dimensional isotropic small‐scale structure.