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Local versus volume-integrated turbulence and mixing in breaking internal waves on slopes

  • Robert S. Arthur (a1) (a2), Jeffrey R. Koseff (a2) and Oliver B. Fringer (a2)

Using direct numerical simulations (DNS), we explore local and volume-integrated measures of turbulence and mixing in breaking internal waves on slopes. We consider eight breaking wave cases with a range of normalized pycnocline thicknesses $k\unicode[STIX]{x1D6FF}$ , where $k$ is the horizontal wavenumber and $\unicode[STIX]{x1D6FF}$ 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 (J. Fluid Mech., vol. 740, 2014, pp. 114–135). Local turbulent mixing efficiencies are calculated using the irreversible flux Richardson number $R_{f}^{\ast }$ and are found to be a function of the turbulent Froude number $Fr_{k}$ . Volume-integrated measures of the turbulent mixing efficiency during wave breaking are also made, and are found to be functions of $k\unicode[STIX]{x1D6FF}$ . The bulk turbulent mixing efficiency ranges from 0.25 to 0.37 and is maximized when $k\unicode[STIX]{x1D6FF}\approx 1$ . In order to connect local and bulk mixing efficiency measures, the variation in the bulk turbulent mixing efficiency with $k\unicode[STIX]{x1D6FF}$ is related to the turbulent Froude number at which the maximum total mixing occurs over the course of the breaking event, $Fr_{k}^{max}$ . We find that physically, $Fr_{k}^{max}$ is controlled by the vertical length scale of billows at the interface during wave breaking.

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