Local vs. Bulk Measures of the Mixing Efficiency in Breaking Internal Waves on Slopes

Using direct numerical simulations, we explore local and bulk measures of the mixing efficiency in breaking internal waves on slopes. In a laboratory-scale domain, we consider eight breaking wave cases with a range of initial pycnocline thicknesses kδ, where k is the horizontal wavenumber and δ is the pycnocline thickness, but with similar incoming wave properties. The energetics of wave breaking is quantified in terms of local turbulent dissipation and irreversible mixing using the method of Scotti & White (2014). Local turbulent mixing efficiencies are calculated using the irreversible flux Richardson number R_f^* and are found to follow a representative function of the turbulent Froude number Fr_k. Comparisons are made to local mixing efficiencies calculated using the traditional flux Richardson number R_f. Because the local mixing efficiency is found to be a weak function of kδ, integrated measures of the turbulent mixing efficiency over the turbulent patch created by wave breaking are also made, and are found to be strong functions of kδ. The bulk patch-integrated turbulent mixing efficiency ranges from 0.25-0.37 and is maximized when kδ≈1, which corresponds to the optimal scale of billows at the interface during breaking, and to the highest occurrence of optimal turbulent Froude numbers Fr_k. Our results suggest that local mixing efficiencies measured during breaking internal wave events in the ocean may not be representative of the bulk mixing efficiency of the event as a whole.