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

Published online by Cambridge University Press:  17 February 2017

Robert S. Arthur Open the ORCID record for Robert S. Arthur [Opens in a new window] ,
Jeffrey R. Koseff  and
Oliver B. Fringer
Robert S. Arthur*
Affiliation:
Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720, USA The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Jeffrey R. Koseff
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
Oliver B. Fringer
Affiliation:
The Bob and Norma Street Environmental Fluid Mechanics Laboratory, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Topographic effects Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 815 , 25 March 2017 , pp. 169 - 198
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Copyright
© 2017 Cambridge University Press 

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