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A Note on the Phillips Spectral Framework for Ocean Whitecaps

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  • 1 School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales, Australia, and Ocean and Climate Physics Division, Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York
  • 2 Ocean and Climate Physics Division, Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York
  • 3 Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada
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Abstract

There has been a recent upsurge in interest in quantifying kinematic, dynamic, and energetic properties of wave breaking in the open ocean, especially in severe sea states. The underpinning observational and modeling framework is provided by the seminal paper of O. M. Phillips. In this note, a fundamental issue contributing to the scatter in results between investigators is highlighted. This issue relates to the choice of the independent variable used in the expression for the spectral density of the mean breaking crest length per unit area. This note investigates the consequences of the different choices of independent variable presently used by various investigators for validating Phillips model predictions for the spectral density of the breaking crest length per unit area and the associated spectral breaking strength coefficient. These spectral measures have a central role in inferring the associated turbulent kinetic energy dissipation rate and the momentum flux to the upper ocean from breaking wave observations.

Lamont-Doherty Earth Observatory Contribution Number 7792.

Corresponding author address: Christopher J. Zappa, Ocean and Climate Physics Division, Lamont-Doherty Earth Observatory, Columbia University, 204E Oceanography, 61 RT 9W, P.O. Box 1000, Palisades, NY 10964. E-mail: zappa@ldeo.columbia.edu

Abstract

There has been a recent upsurge in interest in quantifying kinematic, dynamic, and energetic properties of wave breaking in the open ocean, especially in severe sea states. The underpinning observational and modeling framework is provided by the seminal paper of O. M. Phillips. In this note, a fundamental issue contributing to the scatter in results between investigators is highlighted. This issue relates to the choice of the independent variable used in the expression for the spectral density of the mean breaking crest length per unit area. This note investigates the consequences of the different choices of independent variable presently used by various investigators for validating Phillips model predictions for the spectral density of the breaking crest length per unit area and the associated spectral breaking strength coefficient. These spectral measures have a central role in inferring the associated turbulent kinetic energy dissipation rate and the momentum flux to the upper ocean from breaking wave observations.

Lamont-Doherty Earth Observatory Contribution Number 7792.

Corresponding author address: Christopher J. Zappa, Ocean and Climate Physics Division, Lamont-Doherty Earth Observatory, Columbia University, 204E Oceanography, 61 RT 9W, P.O. Box 1000, Palisades, NY 10964. E-mail: zappa@ldeo.columbia.edu
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