Wave-induced drift in third-order deep-water theory

TL;DR

This paper investigates particle motions beneath deep-water waves up to third-order nonlinearity, comparing classical Stokes drift with improved models incorporating harmonic effects, using numerical simulations.

Contribution

It introduces an enhanced drift approximation that accounts for harmonic effects, improving accuracy over classical Stokes drift in deep-water wave theories.

Findings

Classical Stokes drift slightly underestimates surface drift.

Incorporating harmonic effects improves drift predictions at depth.

Enhanced models better match nonlinear wave theory results.

Abstract

The goal of this work is to investigate particle motions beneath unidirectional, deep-water waves up to the third-order in nonlinearity. A particular focus is on the approximation known as Stokes drift, and how it relates to the particle kinematics as computed directly from the particle trajectory mapping. The reduced Hamiltonian formulation of Zakharov and Krasitskii serves as a convenient tool to separate the effects of weak nonlinearity, in particular the appearance of bound harmonics and the mutual corrections to the wave frequencies. By numerical integration of the particle trajectory mappings we are able to compute motions and resulting drift for sea-states with one, two and several harmonics. We find that the classical Stokes drift formulation provides a slight underestimate of the drift at the surface, and a slight overestimate at depth. Incorporating difference harmonic terms into the formulation yields an improved agreement with the drift obtained from nonlinear wave theories, particularly at greater depth. The consequences of this are explored for regular and irregular waves, as well as parametric wave spectra.