Coastal Wave Generation and Wave Breaking over Terrain: Two Problems in Mesoscale Wave Dynamics

Two problems in mesoscale wave dynamics are addressed: (i) wave-turbulence interaction in a breaking mountain wave and (ii) gravity wave generation associated with coastal heating gradients. The mean and turbulent structures in a breaking mountain wave are considered using an ensemble of high-resolution (essentially LES) wave-breaking 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 ow, where the mean- ow Richardson number is persistently less than 0:25. Computation of the turbulent heat and momentum uxes shows that the dissipation of mean- ow wave energy is due primarily to the momentum uxes. The resulting drag on the leeside shooting ow leads to a loss of mean ow Bernoulli function as well as a cross-stream PV ux. The dependence of both the resolved-scale and subgrid turbulent uxes on the grid spacings is examined by computing a series of ensembles with varying grid spacings. The subgrid parameterization is shown to produce an overestimate of the PV ux at low grid resolution. The generation of gravity waves by coastal heating gradients is explored using linear theory calculations and idealized numerical modeling. The linear theory for ow without terrain shows that the solution depends on two parameters: a nondimensional coastal width L and a nondimensional wind speed U. For U 6= 0 the solution is composed of three distinct wave branches. Two of these branches correspond to the no-wind solution of Rotunno, except with Doppler shifting and dispersion. The third branch exists only for U 6= 0 and is shown to be broadly similar to ow past a steady heat source or a topographic obstacle. The relative importance of this third branch is determined largely by the parameter combination U=L. The e ect of terrain is explored in the linear context using an idealized linear model and associated diagnostic computations. These results are then extended to the nonlinear problem using idealized nonlinear model runs