High‐order oscillatory contributions to shear stress under standing regular wave groups: Theory and experimental evidence

Abstract

[1] In this paper, the oscillatory contributions to the steady shear stress of regular wave groups propagating over plane beds in the laminar regime are investigated theoretically and experimentally. Assuming weak nonlinearity, it was found that weak-unsteady motions induced by regular wave groups and second-order harmonics induced by nonlinear bottom boundary layer (BBL) dynamics contribute to the same order. Wave reflection was found to be an additional mechanism to generate high-order contributions to the steady shear stress. High-order oscillatory contributions to the steady shear stress generate small-amplitude perturbations to the steady streaming through the BBL. As a result, steady secondary circulation cells can be distinguished in the wave group-induced BBL. The magnitude and length scale of the measured small-amplitude perturbations are consistent with the theoretical predictions. Moreover, it is shown that the oscillatory contributions are selected according to their characteristic timescale with distance to the bed. The results could have important implications for understanding BBL dynamics and transport and the transition to the perturbed laminar regime in multiple-scale oscillatory flows.Citation: Sánchez-Badorrey, E., C. Mans, S. Bramato, and M. A. Losada (2009), High-order oscillatory contributions to shear stress under standing regular wave groups: Theory and experimental evidence,