CLOSED-FORM SOLUTIONS FOR THE PROBABILITY DENSITY OF WAVE HEIGHT IN THE SURF ZONE

William R. Dally, Robert G. Dean

Abstract


By invoking the assumption that in the surf zone, random waves behave as a collection of individual regular waves, two closed-form solutions for the probability density function of wave height on planar beaches are derived. The first uses shallow water linear theory for wave shoaling, assumes a uniform incipient condition, and prescribes breaking with a regular wave model that includes both bottom slope and wave steepness effects on the rate of decay. In the second model, the shallow water assumption is removed, and a distribution in wave period (incipient condition) is included. Preliminary results indicate that the models exhibit much of the behavior noted for random wave transformation reported in the literature, including bottom slope and wave steepness effects on the shape of the probability density function.

Keywords


surf zone; probability density of height; closed-form solution

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