AUTHOR=Li Yan , Zheng Zibo , Kalisch Henrik TITLE=Stokes drift and particle trajectories induced by surface waves atop a shear flow JOURNAL=Frontiers in Marine Science VOLUME=11 YEAR=2024 URL=https://www.frontiersin.org/journals/marine-science/articles/10.3389/fmars.2024.1445116 DOI=10.3389/fmars.2024.1445116 ISSN=2296-7745 ABSTRACT=

Surface waves and currents are crucial to the mass transfer in the air-sea interaction as they can drive a variety of dynamical processes. How mass can be transported by surface waves and current coupling is addressed through a study of their induced motions of fluid parcels. To this end, a weakly nonlinear wavetrain is imposed on the background flow whose direction and magnitude are permitted to vary with water depth and second-order features of this configuration are investigated. A leading-order approximation to the Stokes drift is derived, correct to the second order in wave steepness, and applicable to an arbitrarily depth-dependent background flow. The reduced forms of the approximate Stokes drift are provided in a few limiting cases such as a current with an exponential profile or propagating in an orthogonal direction to the wave propagation. Novel features related to the Stokes drift and particle trajectories have been reported for the first time as a result of the rotation induced by the wave and current coupling. A non-vanishing component of the Stokes drift velocity and net-mean displacement of fluid parcels in the span-wise direction to the wave propagation are observed in the cases where a shear current propagates obliquely to the waves direction. A non-monotonic dependence on water depth of the stream-wise component of the Stokes drift is shown, and thereby the largest mass transport induced no longer occurs on the still water surface but some depth beneath. The non-monotonic behavior occurs beyond the regime of the near-irrotational assumption of wave-induced motions. It can also lead to the change of the signs for the stream-wise Stokes drift throughout the water column, and thus an overall cancellation of the integrated mass transport by waves over the water column, indicating that the depth-integrated models can likely lead to underestimated effects of the mass transport which is non-trivial at a local depth. The results from this study have far-reaching impact. The Stokes drift profile is a direct input to the parametrization of the surface waves forcing in ocean circulations and the obliquely propagating Stokes drift can be plausibly responsible for the formation of oblique Langmuir rolls to wave propagation in the open ocean.