On the Stokes drift in traveling surface pulses

Jan Erik H Weber

doi:10.1016/j.ocemod.2021.101847

Abstract

Similar to the Stokes drift in periodic gravity waves, we introduce a second-order Stokes effect on the particle drift in isolated linear surface disturbances (pulses) in shallow water. For a linear disturbance with the shape and length scale of a KdV solitary wave, the model results agree surprisingly well with the observed drift in moderately steep solitary waves in the laboratory, as well as with more comprehensive theory for surface drift in solitary waves.

Highlights

Wave-induced particle drift in shallow water is a phenomenon that is of considerable interest for coastal engineers and environmentalists
The aim of this paper is to study the effect of the Stokes drift in small amplitude non-periodic waves
This is a general result for linear symmetric pulses in shallow water where the effect of the Stokes drift has been taken into account

Summary

Introduction

Wave-induced particle drift in shallow water is a phenomenon that is of considerable interest for coastal engineers and environmentalists. It has an impact on sediment transport as well as the spread of effluents and pollution in the near-shore zone. We follow the approach by Eames and McIntyre (1999) for the Lagrangian displacement due to periodic wave motion, but apply it to isolated surface pulses.

Mathematical derivation

Periodic motion

Non-periodic flows

A solitary wave-like pulse

Concluding remarks