Vertical structure of flows on a shallow reef flat: A coral reef surf zone

Abstract

We present a 1D model of the vertical structure of wave-driven flows on a shallow coral reef and compare that model to observations made on the reef flat on Ofu, American Samoa. This model is based on longstanding approaches to modeling flow structure in beach surf zones including the averaged effects of breaking and broken surface waves. Waves enter the model through an imbalance between the radiation stress and barotropic pressure gradients that exists below the troughs of the waves, which is offset by turbulent shear stress gradients. Assuming that the depth varying eddy viscosity takes the form found in open channel flows, i.e., a parabola, the horizontal momentum equation can be integrated twice with respect to height to derive the distribution with height of the velocity. The resulting theory is compared to observations made on a reef flat located on Ofu, American Samoa. Using a velocity scale in the eddy viscosity model that is proportional to the rms wave velocity, modeled profiles match observations reasonably well (average skill= 0.66), although there is some ambiguity introduced because matching observations and theory requires the addition of a correction that is found to depend on the square of the rms wave height.