Spectral Estimates of Dissipation Rate within and near the Surf Zone

Abstract

Three-dimensional point velocity measurements from within and near the surf zone are used to examine changes in turbulent dissipation rate with location relative to the breakpoint and wave conditions. To separate turbulence from wave orbital currents, dissipation rate is derived using the inertial subrange of the wavenumber spectrum. The measured frequency spectrum is transformed into a wavenumber spectrum by generalizing Taylor's hypothesis to advection of turbulence past a sensor by monochromatic water waves in arbitrary water depth. The resulting dissipation rate is compared with that obtained by averaging the dissipation rates calculated from frequency spectra of very short segments of the time series, over which Taylor's hypothesis for steady currents can be used. The dissipation rate calculated using the latter compares well, in the averaged sense, to the dissipation rate calculated using the whole time series, even though the whole time series includes segments that violate Taylor's assumptions. Measured dissipation rates inside and very near the breakpoint show large increases shoreward and lesser increases with deep-water significant wave height. Farther outside the surf zone, dissipation rate depended on frequency, significant wave height, and depth. Simple models show that the surf-zone patterns are explained by shoreward increases in the probability of wave breaking, although measured turbulence levels are significantly less than needed to dissipate the measured wave energy, suggesting that most of the dissipation occurs above trough level or very near the bed.