Numerical and analytical studies of non-linear gravity-capillary waves in fluid layers under normal electric fields

Document Type

Article

Publication Date

12-1-2007

Abstract

Non-linear gravity-capillary waves travelling at constant speed are considered in the presence of a normal electric field. The fluid, which is assumed to be inviscid, irrotational and a perfect dielectric, is bounded below by a solid plate electrode held at constant voltage, and the region above the free surface is a hydrodynamically passive perfect dielectric, e.g. air. A second parallel flat plate electrode is placed laterally far away and drives a uniform normal electric field there. Electrohydrodynamic coupling occurs at the free surface through the Maxwell stresses which act to modify the normal stress balance and consequently the Bernoulli equation boundary condition there. Three harmonic problems in deforming domains need to be solved, one for the hydrodynamics and one each for the electrostatics above and below the free surface, respectively. We derive and implement an accurate boundary integral method to compute travelling waves of arbitrary wavelength and amplitude. In addition, we consider a long-wave non-linear model of the full problem and compare solutions with the direct simulations. In both cases, we establish the existence of multiple families of solutions extending the classical theory of gravity-capillary waves. An asymptotic theory is also developed to construct periodic waves with ripples. These are used in comparisons with the numerical calculations and the agreement is very good. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Identifier

36649035562 (Scopus)

Publication Title

IMA Journal of Applied Mathematics Institute of Mathematics and Its Applications

External Full Text Location

https://doi.org/10.1093/imamat/hxm040

e-ISSN

14643634

ISSN

02724960

First Page

832

Last Page

853

Issue

6

Volume

72

This document is currently not available here.

Share

COinS