N.V.Saltanov, V.N.Saltanov The Gromeka transformation analog in magnetohedrodynamics of rotating nonhomogeneous fluid |
Applied hydromechanics, Vol. 5 (77) ¹ 1, (2003) |
| The analogue of Gromeka's transformation in the two - dimensional stationary problem of magnetohydrodynamics of nonhomogeneous rotational liquid is realized. The integrals of symmetry are obtained,and using their help the problem is reduced to a single non-linear equation in partial derivatives of the second order, serving for the definition of the current function y. Modified current function F = F(y) is introduced. As a result the problem is reduced to quasilinear equation in partial derivatives of the second order. This equation involves arbitrary functions of its argument: density r(F), analogue of Bernoulli function wem(F), 3 - component of the generalized impulse of liquid unit mass q(F), magnetic potential A(F) and electric potential Fe(F). Arbitrariness in choosing of dependencies r(F), wem(F), q(F), A(F) and Fe(F) can be used for the approximation of the real parameters of continuum. At a certain assignment of these dependencies the equation for the modified current function becomes linear, what shows substantial advantages in a solving of a boundary problems. The waves of finite amplitude in magnetic rotational cylindrical layer of homogenous fluid are considered. |
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KEY WORDS: *** |
| TEXT LANGUAGE: Russian |