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O. M. Phillips
,
Daifang Gu
, and
Mark Donelan

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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O. M. Phillips
,
Daifang Gu
, and
Edward J. Walsh

Abstract

In a previous paper (Phillips et al.) an approximate theory was developed that predicted that the expected configuration of extreme waves in a random sea (or the average configuration of an ensemble of extreme waves) is proportional to the space-time autocorrelation function of the surface displacement of the wave field as a whole. This result is tested by examination of scanning radar altimeter measurements made during SWADE in four different sea states, including a unimodal mature wave field, a short fetch, a wind-generated sea crossing swell, a very broad directional spectrum, and a fetch-limited wind sea with opposing swell. In each of these, the spatial autocorrelation function was found directly from the SRA data. The highest waves in each dataset were selected and their configurations averaged with respect to the crest. These averaged configurations were in each case found to be consistent with the autocorrelation function.

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Daifang Gu
,
S. G. H. Philander
, and
Michael J. McPhaden

Abstract

Data for the period from 1985 to 1993 from TAO moorings along 110°W (5°S–5°N) and 140°W (2°S–9°N) describe the vertical, meridional, and temporal structure of the seasonal cycle of several variables. The results have a number of interesting features. The amplitude of the seasonal cycle is relatively constant in the surface layers but varies considerably at the depth of the equatorial thermocline where it was small before 1989, large thereafter. Also, vertical seasonal movements of the thermocline have little effect on sea surface temperatures. These seasonal variations are consistent with a westward propagating coupled ocean–atmosphere mode in the surface layers. Conversely, the low-frequency modulation of the seasonal cycle in the thermocline is associated with changes in the seasonal cycle of the zonal wind in the central and western tropical Pacific and might be attributable to equatorial Kelvin waves forced resonantly by the surface winds.

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