Phillips' Lambda function: Data summary and physical model

Abstract

Measurements of Phillips' Lambda function describing the average length of breakers on the ocean per unit area at speed cb 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 cb 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.