Characteristics of Turbulence Structure and Undertow in the Surf Zone

Abstract

The characteristic motion of water under breaking waves and the turbulence structure in the surf zone were investigated through detailed two-dimensional velocity measurements in a wave flume. Significant difference was found between the breaking processes in the outer and inner regions of the surf zone. The velocity field in each region consists of steady current, periodic wave motion, organized vortex motion and turbulence. It was found that the organized vortex motion caused by wave breaking was an important fluid motion connecting the wave motion and the turbulence. The vertical profiles of the undertow, which is the steady current below the wave trough level, were investigated from velocity histories measured by hot-film and laser-Doppler-velocimeters. The turbulence generated in the upper layer by wave breaking prevents the development of the bottom boundary layer in the inner region. The vertical distribution of the mean Reynolds stress and the mean eddy viscosity coefficient in the inner region can be approximated by linear functions of the vertical elevation. The offshore-directed mean shear stress on the bottom is so large that it can not be neglected in the modeling of the undertow. The transition point which was the boundary between the outer and inner regions of the surf zone was defined as the offshore limit of the quasi-steady breaking region. The distance from the breaking point to the transition point was expressed in terms of the breaking water depth and the bottom slope. In order to describe the mechanism of the energy transfer during wave breaking accurately, a model was presented in which the organized large vortexes were taken into account as a transmitter of energy in the energy transfer process from wave motion to turbulence. The distribution of the turbulence energy calculated by this model agreed with the experimental results qualitatively. The mass and momentum fluxes by the organized large vortexes were also discussed. The mass transport by breaking waves was found to be induced by the wave motion and the organized large vortexes. By using the models of the energy distribution and the mass transport, a model was presented for the two-dimensional distribution of the undertow. The Reynolds stress and the eddy viscosity coefficient were quantitatively evaluated from the energy dissipation rate on the basis of the dimensional analysis. The variation of the mean water level in the surf zone was also predicted with a good accuracy by considering the momentum flux by the organized vortexes. The model can evaluate the distribution of the undertow on an arbitrary beach topography from the incident wave condition.