Modified Stokes Drift due to Surface Waves and Corrugated Sea-floor Interactions with and without a Mean Current

Abstract:

Ocean surface waves cause floating particles to undergo a slow drift in the direction of propagation of the waves. This forward drift, commonly known as the Stokes drift, plays a crucial role in the transport of various tracer parcels, from sediments to pollutants, in the marine environment. We show that this drift may be significantly affected when an incident intermediate or shallow water surface wave travels over a corrugated sea-floor. The mechanism at work is Bragg resonance -- reflected waves generated via nonlinear resonant interactions between an incident wave and a rippled bottom. First, we theoretically explain the fundamental effect of two counter-propagating Stokes waves on Stokes drift and then perform numerical simulations of Bragg resonance using High-order Spectral method. A monochromatic incident wave on interaction with a rippled patch of bottom topography yields a complex interference between the incident and reflected waves. When the velocity induced by the reflected waves exceeds that of the incident, particle trajectories reverse, leading to a backward drift. Lagrangian and Lagrangian-mean trajectories reveal that parcels on the free surface in the vicinity of the up-wave side of the patch are either trapped or reflected, implying that the rippled patch acts as a non-surface-invasive particle trap or reflector. Parametric analysis is performed by varying the length and amplitude of the rippled patch; reflection, and thus the effectiveness of the patch, increases with increasing ripple's amplitude and patch length. We also include realistic constant mean current and show noticeable differences in Lagrangian-mean trajectories with and without the rippled patch. Theoretical analysis reveals additional terms in the Stokes drift arising from the particular solution due to mean-current and bottom-ripple interactions, irrespective of whether Bragg resonance condition is met. Our analyses may be useful for designing artificial, corrugated sea-floor patches for mitigating microplastics and other forms of ocean pollution. We also expect that sea-floor corrugations, especially in the nearshore region, may significantly affect oceanic tracer transport.