The theory of fifth-order Stokes waves in a linear shear current

TL;DR

This paper derives advanced fifth-order Stokes wave solutions considering linear shear currents, improving accuracy over previous models, and explores how vorticity influences particle trajectories and wave behavior.

Contribution

It introduces a new set of fifth-order Stokes wave solutions incorporating shear currents, validated against experimental and numerical data, enhancing understanding of wave-current interactions.

Findings

Solutions are more accurate in strong currents and vorticity conditions.

Vorticity affects fluid particle trajectories and Stokes drift directions.

Enhanced modeling of wave behavior in shear flows.

Abstract

In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by utilizing the perturbation method originally proposed for pure waves that was recently published. The present solutions are checked against the existing experimental data, the third-order stream function solutions, as well as the numerical results. The comparisons demonstrate that the present solutions are more accurate in describing the velocity distributions during wave propagation, especially in strong following currents and positive vorticity conditions. Subsequently, the present solutions are used to investigate the fluid particle trajectories for different wave-current interaction conditions. The results indicate that the background vorticity can alter the patterns of fluid particle trajectories and the direction of Stokes drifts.