Movement of and drag force on slender flat plates in an array exposed to combinations of unidirectional and oscillatory flow

Abstract

When flexible structures deflect under unidirectional flow or sway under oscillatory flow, their hydrodynamic drag forces are reduced. The flow-induced motion of a structure is governed by the balance between hydrodynamic forces and restoring forces due to stiffness (a ratio known as the Cauchy number, Ca). Movement of and drag on structures under unidirectional (current) and oscillatory (wave) flow have often been studied separately, but such flows frequently coexist. In this study, a simple numerical model of a slender flexible plate, which can represent a seagrass blade, was used to investigate how the posture of and drag on the plate in oscillatory flow was impacted by collinear currents moving in the same (following) and opposite (opposing) directions, relative to the wave propagation. The rate of work done against hydrodynamic drag forces defines the rate of wave energy dissipation, ED,w. The velocity acting on the blade was modeled as if the blade existed in a canopy of blades. For conditions in which blade motion was observed, added currents influenced ED,w in two ways. When the ratio of the time-averaged velocity within the canopy, U1, to the wave velocity amplitude, Uw, was less than 0.33±0.05, ED,w was reduced relative to the pure wave condition, which was attributed to current-induced deflection. However, when U1/Uw exceeded 0.33±0.05, ED,w increased. While the blade increasingly deflected with increasing current, higher currents also limited unsteady wave-induced reconfiguration, increasing the relative motion between the blade and fluid and therefore increasing drag. While Ca can predict the drag reduction associated with weak current, it cannot predict the increase in drag for U1/Uw>0.33. Finally, the model was used to explore the influence of current on wave amplitude evolution across a seagrass meadow. Relative to pure wave conditions, opposing currents enhanced wave damping, but following currents had little impact on wave damping.