Equilibrium ranges in surf zone wave spectra

Abstract

Laboratory measurements of two wave trains breaking on a plane slope demonstrate dramatic changes in spectral shape in the surf zone. The higher‐frequency spectral peak is completely eliminated in the surf zone, and the resulting spectral shape is similar regardless of the peak frequency and relative energy content of the higher‐frequency peak. Examination of both laboratory and field data show that surf zone wave number (k) spectra evolve to contain two equilibrium ranges. The higher‐frequency range is similar to that proposed by Toba in deeper water with the form k−5/2 and is valid for approximately k > 1/depth. The second range falls between the peak wave number and k = 1/depth and has a wave number dependence of k−4/3, similar to that proposed by Zakharov on theoretical grounds. The equilibrium range coefficients, which are a function of wind speed in deep and finite water depths, are a function of the water depth in the surf zone. The laboratory and field data sets used in these analyses covered a broad range of conditions (unidirectional and multidirectional waves, plane and barred beaches, two orders of magnitude variation in wave height, and one order of magnitude variation in wave period), yet the equilibrium ranges identified were consistent and provide a robust parameterization of surf zone wave spectra.