Novosibirsk, Russia, May, 30 – June, 4, 2011

"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

## Peregudin S.I. Kholodova S.E.## Modeling of the process distribution of MHD-waves in rotating layer of an electrically conducting incompressible fluid in an equatorial region## Reporter: Peregudin S.I.The equations describing the three-dimensional equatorial dynamics of an ideal electrically conducting inhomogeneous rotating fluid are studied. The magnetic and velocity fields are represented as superpositions of unperturbed steady-state fields and those induced by wave motion. As a result, after introducing two auxiliary functions, the equations are reduced to a special scalar one. Based on the study of this equation, the solvability of initial–boundary value problems arising in the theory of waves propagating in a spherical layer of an electrically conducting density-inhomogeneous rotating fluid in an equatorial zone is analyzed. Particular solutions of the scalar equation are constructed that describe small-amplitude wave propagation.
The main result of this study is the reduction of the original nonlinear vector system of partial differential equations to a scalar equation and an analytical representation of the solution to the problem of small perturbations propagating in an ideal incompressible stratified electrically conducting fluid in an equatorial region. We constructed the exact solution of the reduced equation describing the limiting case of equatorial dynamics. The analysis presented suggests the existence of nontrivial wave perturbations of the medium near the equator.
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