Dispersive shallow water magnetohydrodynamics
P. J. Dellar Dispersive shallow water
magnetohydrodynamics Phys. Plasmas 10 581-590
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Abstract
Shallow water magnetohydrodynamics (SWMHD) is a recently proposed model
for a thin layer of incompressible, electrically conducting fluid. The
velocity and magnetic field are taken to be nearly two dimensional, with
approximate magnetohydrostatic balance in the perpendicular direction,
leading to a reduced two dimensional model. The SWMHD equations have
been found previously to admit unphysical cusp-like singularities in
finite amplitude magnetogravity waves. This paper extends the
Hamiltonian formulation of SWMHD to construct a dispersively
regularized system, analogous to the Green--Naghdi equations of
hydrodynamics, that supports smooth solitary waves and cnoidal
wavetrains, and shares the potential vorticity conservation properties
of SWMHD.
See P. A. Gilman (2000) Magnetohydrodynamic
"shallow water'' equations for the solar tachocline
Astrophys. J. Lett. 544 pp 79-82
P. J. Dellar (2002) Hamiltonian and symmetric hyperbolic structures of
shallow water magnetohydrodynamics Phys. Plasmas 9 pp
1130-1136
A. E. Green and P. M. Naghdi
(1976) A derivation of equations for wave propagation in water of
variable depth J. Fluid Mech. 78 pp 237-246
J. Miles and R. Salmon (1985) Weakly
dispersive nonlinear gravity-waves J. Fluid Mech. 157
pp 519-531
BibTeX citation information:
@article{DellarDSWMHD,
author = "P. J. Dellar",
title = "Dispersive shallow water magnetohydrodynamics",
year = "2003",
journal = "Phys. Plasmas",
volume = "10",
pages = "581--590",
URL = "http://link.aip.org/link/?PHPAEN/10/581",
DOI = "doi:10.1063/1.1537690"
}
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