Theoretical investigation of current induced by wind shear and waves in fluid of finite depth

Abstract

The current induced by wind and monochromatic waves in a rotating, viscous fluid of finite depth and infinite lateral extent is examined based upon Lagrangian description of motion. The fluid viscosity is assumed constant and the effect of surface shear stress are incorporated in the analysis. The combined wind-and wave-induced drift velocity is found to be composed of a surface wind shear current and a wave-associated mass transport current. The wave-induced surface drift velocity strongly depends on the radio between water depth, h and wavelength, L. For the case of deep water (h/(L )→∞) the direction of the wave-induced surface drift was found to be in the range of 36 to 45 degrees with respected to the direction of the wind. For small h/(L ) ratio the deflection angle was found to be depend on the magnitude of Ekman depth, σ , or specifically the ratio σ/L , For small σ/L , the deflection angle oscillate around 45, angle. The velocity and deflection angle found in this study, in the case of infinite depth, were in confirmity with the solution of Madsen.