The effect of normal electric fields on the Stokes drift

TL;DR

This paper explores how normal electric fields influence Stokes drift in dielectric fluids under periodic waves, revealing that electric fields alter particle velocities without changing trajectory shapes, with energy profiles depending on depth.

Contribution

It introduces a numerical analysis of Stokes drift in electrohydrodynamic flows, a topic previously underexplored, showing electric fields affect particle velocities but not trajectories.

Findings

Electric fields modify particle velocities beneath waves.

Particle energy depends on depth and frame of reference.

Trajectory shapes remain unchanged despite electric field variations.

Abstract

In periodic wave motion, particles beneath the wave undergo a drift in the direction of wave propagation, a phenomenon known as Stokes drift. While extensive research has been conducted on Stokes drift in water wave flows, its counterpart in electrohydrodynamic flows remains relatively unexplored. Addressing this gap, we investigate Stokes drift beneath periodic traveling irrotational waves on a dielectric fluid under the effect of normal electric fields. Through numerical simulations utilizing conformal mapping, we compute particle trajectories and analyze the resultant Stokes drift behaviors beneath periodic traveling waves. Our findings indicate that variations in the electric field impact particle velocities while maintaining trajectory shapes. Moreover, the kinetic energy associated with a particle depends on its depth location and is a non-decreasing convex function in a laboratory frame and a constant in a moving frame, as observed in water wave flows.