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Phillips' Lambda function: Data summary and physical model
Author(s) -
Irisov V.,
Plant W.
Publication year - 2016
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2015gl067352
Subject(s) - lambda , superposition principle , physics , function (biology) , circuit breaker , fourier transform , power function , mathematical analysis , statistical physics , mathematics , quantum mechanics , evolutionary biology , biology
Measurements of Phillips' Lambda function describing the average length of breakers on the ocean per unit area at speed c b are summarized. An expression is developed that fits these data within reasonable bounds. A physical model for the Lambda function is derived based on the assumption that breaking occurs when the surface steepness exceeds a threshold value. The energy contained in the breaking region is related to the fifth power of the breaker speed, as Phillips showed, and from this the probability of finding a breaker with a speed c b may be determined from a simulation of the long‐wave surface based on a linear superposition of Fourier components. This probability is directly related to the Lambda function so that a form for this function can be determined. The Lambda function so determined agrees in both shape and intensity with the fit to the measured Lambda functions.