Stokes' Drift of linear Defects

TL;DR

This paper investigates how a linear elastic string experiences Stokes' drift when diffusing on a substrate with a traveling wave, revealing a threshold behavior influenced by wave, damping, and temperature parameters.

Contribution

It introduces a theoretical model describing the threshold and diffusion characteristics of Stokes' drift for linear defects on a substrate with a traveling wave.

Findings

Existence of a sharp threshold for Stokes' drift depending on system parameters

Excess diffusion of the string's center of mass at drift onset

Potential anomalous growth in dispersion around the center of mass

Abstract

A linear defect, viz. an elastic string, diffusing on a planar substrate traversed by a travelling wave experiences a drag known as Stokes' drift. In the limit of an infinitely long string, such a mechanism is shown to be characterized by a sharp threshold that depends on the wave parameters, the string damping constant and the substrate temperature. Moreover, the onset of the Stokes' drift is signaled by an excess diffusion of the string center of mass, while the dispersion of the drifting string around its center of mass may grow anomalous.