Ovsyannikov plane vortex: The equations of the submodel |
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Authors: | S V Golovin |
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Institution: | (1) Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia |
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Abstract: | A submodel of the equations of ideal magnetohydrodynamics is constructed that generalizes the classical motion of an ideal
continuous medium with plane waves. It is shown that, in contrast to classical motion, in this submodel the velocity and magnetic-field
vectors can change direction in a plane orthogonal to a distinguished spatial direction. The submodel is described by a system
of equations with two independent variables and a finite relation specifying the orientation of the vector fields in space.
The solutions of the submodel define substantially spatial processes and singularities in the motion of continuous media which
cannot be studied in the classical one-dimensional formulation.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 27–40, September–October, 2008. |
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Keywords: | ideal magnetohydrodynamics partially invariant solutions overdetermined systems of differential equations singularities in the motion of a continuous medium |
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