Gravity wave breaking in two and three dimensions: 2. Three‐dimensional evolution and instability structure

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Abstract
A companion paper by Andreassen et al. (this issue) introduced and used a nonlinear, compressible, spectral collocation code to address the relative evolutions of two‐dimensional motions obtained in two‐ and three‐dimensional simulations of gravity wave breaking. That study illustrated the effects of instability on the wave field and mean flow evolution and suggested that two‐dimensional models are unable to fully describe the physics of the wave breaking process. The present paper examines in detail the structure, evolution, and energetics of the three‐dimensional motions accounting for wave instability as well as their associated transports of momentum and heat. It is found that this instability comprises counterrotating vortices which evolve very rapidly within the convectively unstable region of a breaking wave. Instability scales are selected based on wave geometry and vortices are elongated in the streamwise direction (horizontal wavenumber in the spanwise direction) and result in the rapid collapse of superadiabatic regions within the wave field. The resulting spectra show clearly the transition from gravity wave forcing of harmonics of the incident wave to instability onset and evolution. Fluxes of momentum and heat by the instability reveal the manner in which the gravity wave amplitude is constrained and the influences of instability on the wave transports of these quantities. The breakdown of the instability structure and its evolution toward isotropic small‐scale structure is the subject of the companion paper by Isler et al. (this issue).