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Strong Turbulence in the Wave Crest Region

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  • 1 University of Victoria, Victoria, British Columbia, Canada
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Abstract

High-resolution vertical velocity profiles in the surface layer of a lake reveal the turbulence structure beneath strongly forced waves. Dissipation rates of turbulence kinetic energy are estimated based on centered second-order structure functions at 4-Hz sampling. Dissipation rates within nonbreaking wave crests are on average 3 times larger than values found at the same distance to the free surface but within the wave trough region. This ratio increases to 18 times for periods with frequent wave breaking. The depth-integrated mean dissipation rate is a function of the wave field and correlates well with the mean wave saturation in the wave band ωpω ≤ 4ωp. It shows a clear threshold behavior in accordance with the onset of wave breaking. The initial bubble size distribution is estimated from the observed distribution of energy dissipation rates, assuming the Hinze scale being the limiting size. This model yields the slope of the size distribution, , consistent with laboratory results reported in the literature, and implies that bubble fragmentation associated with intermittent high dissipation rates is a valid mechanism for the setup of bubble size spectra.

Corresponding author address: Johannes Gemmrich, Dept. of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, BC V8W 3P6, Canada. Email: gemmrich@uvic.ca

Abstract

High-resolution vertical velocity profiles in the surface layer of a lake reveal the turbulence structure beneath strongly forced waves. Dissipation rates of turbulence kinetic energy are estimated based on centered second-order structure functions at 4-Hz sampling. Dissipation rates within nonbreaking wave crests are on average 3 times larger than values found at the same distance to the free surface but within the wave trough region. This ratio increases to 18 times for periods with frequent wave breaking. The depth-integrated mean dissipation rate is a function of the wave field and correlates well with the mean wave saturation in the wave band ωpω ≤ 4ωp. It shows a clear threshold behavior in accordance with the onset of wave breaking. The initial bubble size distribution is estimated from the observed distribution of energy dissipation rates, assuming the Hinze scale being the limiting size. This model yields the slope of the size distribution, , consistent with laboratory results reported in the literature, and implies that bubble fragmentation associated with intermittent high dissipation rates is a valid mechanism for the setup of bubble size spectra.

Corresponding author address: Johannes Gemmrich, Dept. of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, BC V8W 3P6, Canada. Email: gemmrich@uvic.ca

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