Wave–Turbulence Interactions in a Breaking Mountain Wave

Abstract

The mean and turbulent structures in a breaking mountain wave are considered through an ensemble of high-resolution (essentially large-eddy simulation) wave-breaking calculations. Of particular interest are the turbulent heat and momentum fluxes in the breaking wave and their roles in shaping the wave-scale and larger-scale flows. The evolution of the breaking wave in the ensemble mean is found to be broadly consistent with prior low-resolution calculations. A turbulent kinetic energy budget for the wave shows that the turbulence production is almost entirely due to the mean shear. Most of the production is at the top of the leeside shooting flow, where the mean-flow Richardson number is persistently less than 0.25. The turbulent dissipation of mean-flow wave energy is shown to result mainly from the turbulent momentum fluxes—specifically, from the tendency of these fluxes to act counter to the mean-flow disturbance wind. Of particular importance is the eddy deceleration of the leeside shooting flow. The resulting momentum dissipation leads to a mean-flow Bernoulli loss, a cross-stream mean-flow PV flux, and a permanent upward mean-flow vorticity transfer. The dependence of the turbulent fluxes on grid spacing is considered by computing a series of ensembles with grid spacings ranging from L/56 to L/3.7 (where L is the mountain half-width). At the highest resolution, the eddy fluxes are mostly resolved, but with increasing grid spacing, the resolved-scale fluxes decline and the parameterized fluxes become larger. It is shown that for the chosen parameter values, the parameterized fluxes overestimate the mean-flow PV flux: at L/3.7 the PV flux is nearly twice that computed at L/56.