Gravity wave breaking in two and three dimensions: 1. Model description and comparison of two‐dimensional evolutions

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Abstract
A nonlinear, compressible, spectral collocation code is employed to examine gravity wave breaking in two and three spatial dimensions. Two‐dimensional results exhibit a structure consistent with previous efforts and suggest wave instability occurs via convective rolls aligned normal to the gravity wave motion (uniform in the spanwise direction). Three‐dimensional results demonstrate, in contrast, that the preferred mode of instability is a series of counterrotating vortices oriented along the gravity wave motion, elongated in the streamwise direction, and confined to the region of convective instability within the wave field. Comparison of the two‐dimensional results (averaged spanwise) for both two‐ and three‐dimensional simulations reveals that vortex generation contributes to much more rapid wave field evolution and decay, with rapid restoration of near‐adiabatic lapse rates and stronger constraints on wave energy and momentum fluxes. These results also demonstrate that two‐dimensional models are unable to describe properly the physics or the consequences of the wave breaking process, at least for the flow parameters examined in this study. The evolution and structure of the three‐dimensional instability, its influences on the gravity wave field, and the subsequent transition to quasi‐isotropic small‐scale motions are the subjects of companion papers by Fritts et al. (this issue) and Isler et al. (this issue).