Turbulence and mixing in unsteady breaking surface waves

Abstract

Laboratory measurements of the post-breaking velocity field due to unsteady deep-water breaking are presented. Digital particle image velocimetry (DPIV) is used to measure the entire post-breaking turbulent cloud with high-resolution imagery permitting the measurement of scales fromO(1m) down toO(1mm). Ensemble-averaged quantities including mean velocity, turbulent kinetic energy (TKE) density and Reynolds stress are presented and compare favourably with the results of Melville, Veron & White (J. Fluid Mech., vol. 454, 2002, pp. 203–233; MVW). However, due to limited resolution, MVW's measurements were not spatially coherent across the turbulent cloud, and this restricted their ability to compute turbulent wavenumber spectra. Statistical spatial quantities including the integral length scaleL11, Taylor microscale λfand the Taylor microscale Reynolds numberReλare presented. Estimation of an eddy viscosity for the breaking event is also given based on analysis of the image data. Turbulent wavenumber spectra are computed and within 12 wave periods after breaking exhibit what have been termed ‘spectral bumps’ in the turbulence literature. These local maxima in the spectra are thought to be caused by an imbalance between the transport of energy from large scales and the dissipation at small scales. Estimates of the dissipation rate per unit mass are computed using both direct and indirect methods. Horizontally averaged terms in the TKE budget are also presented up to 27 wave periods after breaking and are discussed with regard to the dynamics of the post-breaking flow. Comparisons of the TKE density in the streamwise and cross-stream planes with the three-dimensional full TKE density are given in an appendix.