Reynolds Stresses and Velocity Distributions in a Wave-Current Coexisting Environment

Abstract

To investigate changes in the mean velocity profile owing to the interaction between waves and a current, the horizontal and vertical velocity components in the oscillating fluid were measured by a two-dimensional laser anemometer in a recirculating wave tank. The observed instantaneous velocity data concerning waves following and opposing a current were analyzed to obtain the Eulerian-mean velocity, the wave-current Reynolds stress, and the wave-current turbulent intensities. The wave-current Reynolds stress behaves differently when current direction changes. The general characteristic of the Eulerian-mean velocity is greatly affected by the wave-current Reynolds stress. The mean velocity for waves following (opposing) a current is reduced (increased) towards the free surface, when compared with the logarithmic profile. These velocity data were used to verify the results by velocity equations based on the phase-averaged Prandtl momentum-transfer theory. In addition, measurement of water-surface elevations revealed that the phase-averaged waveform for a pure wave is peaked near the crest but flatter near the trough and the variation of the water surface is well predicted by the third-order Stokes wave equation. The original pattern of the waveform varies due to the wave-current interaction, but the current direction only minimally affects the attenuation of the surface waves.