- · Electronic Refereed Journal Article (HTML)
- · Full Refereed Journal Article (PDF/Postscript)
- · References in the article
- · Translate This Page
|Title:||Two-dimensional surface waves in magnetohydrodynamics|
|Affiliation:||AA(Warwick Manufacturing Group, University of Warwick, Coventry CV4 7AL, UK https://orcid.org/0000-0003-3802-3892)|
|Publication:||Journal of Plasma Physics, Volume 85, Issue 4, id.905850405|
|Keywords:||plasma waves, astrophysical plasmas, plasma flows|
|Abstract Copyright:||2019: Cambridge University Press|
The study of nonlinear waves in water has a long history beginning with
the seminal paper by Korteweg & de Vries (Phil. Mag., vol. 39, 1895,
p. 240) and more recently for magnetohydrodynamics Danov & Ruderman
(Fluid Dyn., vol. 18, 1983, pp. 751-756). The appearance of a Hilbert
transform in the nonlinear equation for magnetohydrodynamics (MHD)
distinguishes it from the water wave model description. In this paper,
we are interested in examining weakly nonlinear interfacial waves in
dimensions. First, we determine the wave solution in the linear case.
Next, we derive the corresponding generalisation for the
Kadomtsev-Petviashvili (KP) equation with the inclusion of an
equilibrium magnetic field. The derived governing equation is a
generalisation of the Benjamin-Ono (BO) equation called the Benjamin
equation first derived in Benjamin (J. Fluid Mech., vol. 245, 1992, pp.
401-411) and in the higher-dimensional context in Kim & Akylas (J.
Fluid Mech., vol. 557, 2006, pp. 237-256).