A look at the ensemble-mean structure of a breaking mountain wave

The mean and turbulent structure of a breaking mountain wave is considered through an ensemble average of 20 high-resolution wave-breaking simulations for y-periodic flow past an infinitely long ridge. Particular emphasis is given to the production of small-scale turbulence in the wave and the role of the associated heat and momentum fluxes in establishing the mean flow structure.

Preliminary work shows that the turbulent kinetic energy (TKE) in the breaking wave is distributed mainly along the phase line for which the mean isentropes reach their maximum downward displacement. Comparison to the Richardson number (Ri) of the mean flow shows that this region of high TKE is mostly localized to areas where Ri < 1. However, regions with both low Ri (Ri < 0.5) and no TKE as well as high Ri (Ri > 1) and significant TKE are both found to be present. The vertical momentum flux associated with the turbulence is predominately positive as momentum is distributed upward from the highly accelerated lee-slope flow to the decelerated wake flow aloft. The corresponding heat flux is downward and acts to warm the lee-slope flow and cool the flow at the bottom of the wake. The role of these heat and momentum fluxes in establishing the mean-flow structure is discussed both in terms of PV flux diagnostics and the associated cross-isentrope flux of cross-stream vorticity.

Finally the turbulent fluxes computed from the high-resolution ensemble are used to evaluate the fluxes predicted by the commonly used Smagorinsky-Lilly turbulence parameterization. The parameterization dependence on grid spacing is considered and the optimal values of free parameters (mixing coefficient and Prandtl number) are discussed.