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Expected Structure of Extreme Waves in a Gaussian Sea. Part I: Theory and SWADE Buoy Measurements

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  • 1 Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland
  • | 2 National Water Research Institute, Canada Centre for Inland Waters, Burlington, Ontario, Canada
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Abstract

This paper is concerned with the expected configuration in space and time surrounding extremely high crests in a random wave field, or, equivalently, the mean configuration averaged over realizations of extreme events. A simple, approximate theory is presented that predicts that the mean configuration ζ¯(x + r, t + τ) surrounding a crest at (x, t) that is higher than γσ (where σ is the overall rms surface displacement and γ ≫ 1), when normalized by ζ¯(x,t) for ζ > γσ, is the space-time autocorrelation function ρ(r, t) = ¯ζ(x, t)ζ(x + r, t + τ)/ ζ¯2 for the entire wave field. This extends and simplifies an earlier result due to Boccotti and is consistent with a precise calculation of the one-dimensional case with r = 0, involving the time history of measurements at a single point. The results are compared with buoy data obtained during the Surface Wave Dynamics Experiment and the agreement is found to be remarkably good.

Abstract

This paper is concerned with the expected configuration in space and time surrounding extremely high crests in a random wave field, or, equivalently, the mean configuration averaged over realizations of extreme events. A simple, approximate theory is presented that predicts that the mean configuration ζ¯(x + r, t + τ) surrounding a crest at (x, t) that is higher than γσ (where σ is the overall rms surface displacement and γ ≫ 1), when normalized by ζ¯(x,t) for ζ > γσ, is the space-time autocorrelation function ρ(r, t) = ¯ζ(x, t)ζ(x + r, t + τ)/ ζ¯2 for the entire wave field. This extends and simplifies an earlier result due to Boccotti and is consistent with a precise calculation of the one-dimensional case with r = 0, involving the time history of measurements at a single point. The results are compared with buoy data obtained during the Surface Wave Dynamics Experiment and the agreement is found to be remarkably good.

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