A simple mixing scheme for models that resolve breaking internal waves

Breaking internal waves in the vicinity of topography can reach heights of over 100. m and are thought to enhance basin-wide energy dissipation and mixing in the ocean. The scales at which these waves are modelled often include the breaking of large waves (10. s of meters), but not the turbulence dissipation scales (centimeters). Previous approaches to parameterize the turbulence have been to use a universally large viscosity, or to use mixing schemes that rely on Richardson-number criteria.A simple alternative is presented that enhances mixing and viscosity in the presence of breaking waves by assuming that dissipation is governed by the equivalence of the density overturning scales to the Ozmidov scale (ε=L_T²N³, where LT is the size of the density overturns, and N the stratification). Eddy diffusivities and viscosities are related to the dissipation by the Osborn relation (K_z=ΓεN^-2) to yield a simple parameterization K_z=ΓL_T²N, where Γ≈0.2 is the flux coefficient. This method is compared to previous schemes for flow over topography to show that, when eddy diffusivity and viscosity are assumed to be proportional, it dissipates the correct amount of energy, and that the dissipation reported by the mixing scheme is consistent with energy losses in the model. A significant advantage of this scheme is that it has no tunable parameters, apart from the turbulent Prandtl number and flux coefficient. A disadvantage is that the overturning scales of the turbulence must be relatively well-resolved.