Modeling Effect of Intersection Angle on Near-Bed Flows for Waves and Currents

Abstract

The flow behavior of turbulent wave boundary layers with weak currents was described using a numerical model. Horizontal velocities, shear stresses, turbulent eddy viscosities, and apparent roughnesses were described. The numerical model is based upon the fluid continuity and momentum equations in the vertical plane. The momentum equations retain the advection terms with vertical orbital velocity in contrast to previous numerical models. The horizontal velocities were calculated from the momentum equations, and the vertical orbital velocity distribution was obtained from the continuity equation. The Reynolds terms were modeled by a mixing length hypothesis. The model was compared with existing models for the wave friction factor by switching off the advection terms and produced similar answers to two existing models. Next, the model was applied to a wave-only flow case with the advection terms retained. The model reproduced the measured mass transport profile by van Doorn and Godefroy reasonably well. The model was then applied to wave-current flow cases with arbitrary intersection angles. The model results for 0°, 180°, and 90° agreed well with measurements by van Doorn and Godefroy and van der Stel and Visser, respectively. The model produced significant differences between the following and opposing current cases for the same wave condition. The model results suggest that the wave boundary layer flows for relatively strong waves and weak currents can be accurately described by taking account of the nonlinear advection terms by means of the vertical wave orbital velocity.