Published 6 issues per year
ISSN Print: 2152-5102
ISSN Online: 2152-5110
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On Some Transformations and Approximations of Magnetohydrodynamic Equations
ABSTRACT
Investigations related to some hidden symmetry properties of the system of differential equations of magnetohydrodynamics (MHD) are presented. The MHD-equations of a finite electrical conductivity characterized by the magnetic Reynolds number Rem are considered. Each model under consideration is characterized some hidden geometric and physical symmetry. As a result, it makes it possible to simplify the original model: decomposition, introduction of potentials or new variables, self-similarity et al. The MHD-system for magneto-isotropic compressible fluid under the action of a magnetic field is considered and nondi-mensionalized. It is shown that in the case of one-dimensional nonlinear motion the original system can be reduced to some simplified form. In the case of linearized equations the self-similarity analysis is applied allowing to obtain the system in which the value Rem is not involved explicitly. Approximations of a weak and high Rem are developed leading to hierarchy systems. The introduction of potentials leading to some cases of solvability is presented.