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Non-linear ring waves in a thin layer of magnetic fluid with variable thickness

A. N. Golubyatnikov

Lomonosov Moscow State University, Research Institute of Mechanics, 1 Michurinsky pr., 119192 Moscow, Russian Federation

In the ``shallow water" approximation, the problem of propagation of non-linear ring waves with relatively small amplitudes in a thin layer of paramagnetic fluid with variable depth exposed to a non-uniform magnetic field is considered. The equations of motion that have a variational feature are derived. An exact method of solution for the problem with weak discontinuity has been developed. The problem with a weak shock wave is solved as an approximation to this solution. An example of wave propagation at the equilibrium initial state is considered. Figs 1, Refs 12.

Magnetohydrodynamics 55, No. 3, 287-294, 2019 [PDF, 0.17 Mb]

Copyright: Institute of Physics, University of Latvia
Electronic edition ISSN 1574-0579
Printed edition ISSN 0024-998X