A new application of the Korteweg-de Vries Benjamin-Ono equation in interfacial electrohydrodynamics

Document Type

Article

Publication Date

1-1-2007

Abstract

We consider waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. We use perturbation theory to identify canonical scalings and to derive a Korteweg-de Vries Benjamin-Ono equation arising in interfacial electrohydrodynamics. When the Bond number is equal to 1/3, dispersion disappears and the equation reduces to the Benjamin-Ono equation. In the additional limit of vanishing electric fields, we show how to obtain a new evolution equation that contains third- and fifth-order dispersion as well as a nonlocal electric field term. © 2007 American Institute of Physics.

Identifier

34047208577 (Scopus)

Publication Title

Physics of Fluids

External Full Text Location

https://doi.org/10.1063/1.2716763

ISSN

10706631

Issue

3

Volume

19

Grant

DMS-0405639

Fund Ref

National Science Foundation

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