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Experimental Investigation of Wave Breaking Criteria Based on Wave Phase Speeds

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  • 1 Department of Civil and Offshore Engineering, Heriot-Watt University, Edinburgh, Scotland
  • | 2 Department of Ship and Marine Technology, University of Strathclyde, Glasgow, Scotland
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Abstract

Experiments were performed that test the kinematic breaking criterion, which states that the horizontal fluid particle velocity at the surface of a crest exceeds the local phase speed of the crest prior to breaking. Three different definitions of phase speed are used to calculate phase velocities of the wave crests from detailed surface elevation measurements. The first definition, based on the equivalent linear wave, is constant over the wavelength of the wave. The second, based on partial Hilbert transforms of the surface elevation data, is local in space and time giving instantaneous values at all space and time measurements. The third, based on the speed of the position of the crest maximum, is local in time but not in space. Particle image velocimetry is used to obtain horizontal components of fluid particle velocity at the surface of crests of breaking and nonbreaking waves produced in a wave flume using the chirp-pulse focusing technique. The ratios of these fluid particle speeds to crest phase speeds are calculated and are consistently less than unity. The speed ratio for the rounded crest of a plunging breaker is at most 0.81, implying that the kinematic breaking criterion is far from satisfied. The ratio for the more sharply pointed crest of a spilling breaker is at most 0.95, implying that the kinematic breaking criterion is closer to being satisfied. Thus, for the breaking waves in this study the kinematic breaking criterion is not satisfied for any of the three definitions of phase speed and so it cannot be regarded as a universal predictor of wave breaking.

Corresponding author address: Dr. Paul Stansell, Department of Civil and Offshore Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland. Email: p.stansell@hw.ac.uk

Abstract

Experiments were performed that test the kinematic breaking criterion, which states that the horizontal fluid particle velocity at the surface of a crest exceeds the local phase speed of the crest prior to breaking. Three different definitions of phase speed are used to calculate phase velocities of the wave crests from detailed surface elevation measurements. The first definition, based on the equivalent linear wave, is constant over the wavelength of the wave. The second, based on partial Hilbert transforms of the surface elevation data, is local in space and time giving instantaneous values at all space and time measurements. The third, based on the speed of the position of the crest maximum, is local in time but not in space. Particle image velocimetry is used to obtain horizontal components of fluid particle velocity at the surface of crests of breaking and nonbreaking waves produced in a wave flume using the chirp-pulse focusing technique. The ratios of these fluid particle speeds to crest phase speeds are calculated and are consistently less than unity. The speed ratio for the rounded crest of a plunging breaker is at most 0.81, implying that the kinematic breaking criterion is far from satisfied. The ratio for the more sharply pointed crest of a spilling breaker is at most 0.95, implying that the kinematic breaking criterion is closer to being satisfied. Thus, for the breaking waves in this study the kinematic breaking criterion is not satisfied for any of the three definitions of phase speed and so it cannot be regarded as a universal predictor of wave breaking.

Corresponding author address: Dr. Paul Stansell, Department of Civil and Offshore Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland. Email: p.stansell@hw.ac.uk

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