{"title":"Wind-Wave Breaking","authors":"W. Kendall Melville","doi":"10.1016/j.piutam.2018.03.004","DOIUrl":null,"url":null,"abstract":"<div><p>Rational models of wind-wave growth were proposed in the 1950s (Miles 1957, Phillips 1957), theories of wave-wave interactions (Phillips 1960, Hasselmann 1962, Zakharov 1968) and wave-action conservation for waves in fluids (Whitham 1965, Bretherton and Garrett 1969) in the 1960s, but it was not until the 1980s that laboratory experiments (Duncan 1981, Melville and Rapp 1985) and a seminal paper by Owen Phillips in 1985 on a model of the equilibrium range in wind-wave spectra, and a formulation of breaking, began a rational program of research into the role of breaking in surface wave kinematics and dynamics. Two important features of Phillips’ 1985 paper were the introduction of Λ(c)dc, the average total length of breaking fronts per unit area of ocean moving with velocities in the range (c, c + dc) and the statement that the average rate of energy loss per unit area by breakers in the same velocity range was given by</p><p><span><math><mrow><msub><mrow><mi>ɛ</mi></mrow><mi>b</mi></msub><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mi>d</mi><mi>c</mi><mo>=</mo><mi>b</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mi>ρ</mi><msup><mi>g</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><msup><mi>c</mi><mn>5</mn></msup><mstyle><mi>Λ</mi></mstyle><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mi>d</mi><mi>c</mi></mrow></math></span></p><p>where b is a dimensionless breaking strength and g is gravity. The energy loss per unit length of breaker, <em>b</em>ρ<em>g<sup>-1</sup>c<sup>5</sup></em>, was based on Duncan’s work, but anticipated in part by Lighthill (1978). Lower order moments of Λ(c) describe kinematical features of breaking up to the third moment, with the fourth moment describing the momentum flux from waves to currents. The structure of the dissipation equation imposes a combination of different approaches to quantifying it. Estimates of b have depended on arguments based on Taylor’s (1935) inertial scaling of turbulence dissipation, supported by laboratory experiments and recent DNS and LES numerical experiments, while Λ(c) over any significant dynamical range can only be measured in the field. The success of the early attempts to follow this approach has led to recent work on air entrainment for gas transfer, and theoretical uses of fundamental vortex dynamics to develop our knowledge of the role of breaking in air-sea interaction. In this paper I will review the material from the laboratory, through scaling arguments, modeling and field measurements.</p></div>","PeriodicalId":74499,"journal":{"name":"Procedia IUTAM","volume":"26 ","pages":"Pages 30-42"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.piutam.2018.03.004","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Procedia IUTAM","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S221098381830004X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Rational models of wind-wave growth were proposed in the 1950s (Miles 1957, Phillips 1957), theories of wave-wave interactions (Phillips 1960, Hasselmann 1962, Zakharov 1968) and wave-action conservation for waves in fluids (Whitham 1965, Bretherton and Garrett 1969) in the 1960s, but it was not until the 1980s that laboratory experiments (Duncan 1981, Melville and Rapp 1985) and a seminal paper by Owen Phillips in 1985 on a model of the equilibrium range in wind-wave spectra, and a formulation of breaking, began a rational program of research into the role of breaking in surface wave kinematics and dynamics. Two important features of Phillips’ 1985 paper were the introduction of Λ(c)dc, the average total length of breaking fronts per unit area of ocean moving with velocities in the range (c, c + dc) and the statement that the average rate of energy loss per unit area by breakers in the same velocity range was given by
where b is a dimensionless breaking strength and g is gravity. The energy loss per unit length of breaker, bρg-1c5, was based on Duncan’s work, but anticipated in part by Lighthill (1978). Lower order moments of Λ(c) describe kinematical features of breaking up to the third moment, with the fourth moment describing the momentum flux from waves to currents. The structure of the dissipation equation imposes a combination of different approaches to quantifying it. Estimates of b have depended on arguments based on Taylor’s (1935) inertial scaling of turbulence dissipation, supported by laboratory experiments and recent DNS and LES numerical experiments, while Λ(c) over any significant dynamical range can only be measured in the field. The success of the early attempts to follow this approach has led to recent work on air entrainment for gas transfer, and theoretical uses of fundamental vortex dynamics to develop our knowledge of the role of breaking in air-sea interaction. In this paper I will review the material from the laboratory, through scaling arguments, modeling and field measurements.
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