Three‐dimensional streaming in the seabed boundary layer beneath propagating waves with an angle of attack on the current

Abstract

The effect of three‐dimensional wave‐induced streaming on the seabed boundary layer is investigated for following and opposing waves and current where the wave propagation forms a nonzero angle with the current. It is shown that the seabed boundary layer flow results from an interaction between the classical wave‐current interaction (reducing the mean velocity relative to current alone), Longuet‐Higgins streaming (forcing the flow in the wave propagation direction), and streaming caused by turbulence asymmetry in successive wave half‐cycles (forcing the flow against the wave propagation direction). For waves and current which are not colinear, the mean velocity profile exhibits a veering behavior which is strongly affected by streaming, particularly for the most wave‐dominated situations. The effect of streaming on the boundary layer flow has been investigated for different wave‐current conditions and bottom roughnesses. Visualizations are given by mean Eulerian and Lagrangian velocity profiles, as well as three‐dimensional seabed boundary layer particle trajectories. The effect of streaming decreases as the flow becomes more current dominated. The mean velocity in the current direction decreases as the roughness increases. However, the mean velocity orthogonal to the current direction increases as the roughness increases due to the lack of wave‐current interaction in this direction. An excellent agreement between the predicted and recently measured velocity profiles beneath horizontally uniform asymmetric forcing is obtained.

Analysis of Observed Streaming in Field Measurements

“…An equivalent wave has been applied to represent the random waves using the rms (root-mean-square) value of the measured velocity amplitude. The present model has earlier been successfully applied on seabed boundary layers (regular and random waves plus current) by Holmedal et al (2003) and on sediment transport (Holmedal et al 2004;Holmedal and Myrhaug 2006;Holmedal and Myrhaug 2009;Holmedal et al 2013;Afzal et al 2015); a convincing agreement between measurements and predictions of turbulent flow quantities and sediment concentration was obtained. The governing equations for conservation of momentum and mass are given as:…”

Effect of bottom roughness on sediment transport due to streaming beneath linear propagating waves with an angle of attack on current

“…They studied the interaction between the classical wave-current interaction mechanism and the two streaming mechanisms, also affecting the direction and veering of the resulting current, which cannot be measured neither in closed channels nor in large wave flumes. Overall, Afzal et al (2015b) yields new insight into wave-current seabed boundary layer flow characteristics.…”

“…Other studies such as Holmedal & Myrhaug (2009) have focused on sediment transport due to the Longuet-Higgins streaming mechanism under waves alone, while Holmedal et al (2013) have focused on following and opposing waves and current. Recently, Afzal et al (2015b) investigated the effect of streaming on the wave-current sea bed boundary layer for waves with an angle of attack on the current using numerical simulations. They studied the interaction between the classical wave-current interaction mechanism and the two streaming mechanisms, also affecting the direction and veering of the resulting current, which cannot be measured neither in closed channels nor in large wave flumes.…”

Turbulent boundary layers under irregular waves and currents: Experiments and the equivalent‐wave concept

“…[] and Afzal et al . [], among others, numerically showed that the effects of both progressive and turbulent asymmetry streamings on wave‐current interactions can be very significant.…”

“…Yuan and Madsen [2015] (YM15 hereafter) reported experiments of currents in the presence of asymmetry oscillatory flows and showed that the turbulence asymmetry streaming has a pronounced effect on currents, which can even invalidate the basic wave-current interaction proposed by the GM model. Holmedal et al [2013] and Afzal et al [2015], among others, numerically showed that the effects of both progressive and turbulent asymmetry streamings on wave-current interactions can be very significant.…”