N.V.Saltanov Generalized potentials in magnetohydrodynamics and rotating fluid dynamics |
Applied hydromechanics, Vol. 2 (74) ¹ 4, (2000) |
| Based on generalized potentials the general solution of the linearized system of magnetohydrodynamic equations of an ideally conductive fluid in a ststionary magnetic field is represented in terms of general solutions of two homogeneous wave equations with Alfven signal propagation speed and a general solution of the Laplace equation. Transformation of the linearized system of magnetohydrodynamic equations of a dissipative conductive fluid in stationary magnetic field is performed. If the cyclic coordinate exists the system of magnetohydrodynamic equations of dissipative rotating fluid in nonlinear case is reduced to the system of four partial differential nonlinear equations required for finding of the stream function, the magnetic analog of it and the third components of speed and magnetic field. This system is noted to transform into the known one at the absence of rotation. The linearized system of equations of rotating fluid dynamics in the "shallow-water" approximation is reduced to the one linear partial differential equation of third order that define the generalized potential. Based on the obtained equation for generalized potential the problem of seichual oscillations in a reservoir is considered when the reservoir depth is a piecewise function of a cross coordinate. Comparison between the obtained results and the results of other authors is performed. |
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| TEXT LANGUAGE: Russian |