Investigation of magnetohydrodynamical shock waves propagation in nonhomogeneous plasma medium by Whitham method

Abstract

The propagation of a plane magnetohydrodynamical shock wave in non-homogeneous plasma medium is considered. The investigation is based on Whitham method which was used for the case of transverse magnetic field. The differential equation for the shock wave velocity front as a function of the coordinate along the propagation path was derived. The numerical solution was obtained in the case of the wave propagating in adiabatic atmosphere. On the basis of jump relations the characteristics (velocity, preassure, density) behind the wave were obtained at arbitrary magnetic field and initial Mach number. It is shown that a magnetohydrodynamical shock wave accelerates in comparison with an ordinary one at small values of magnetic parameter  . At large values of  the influence of magnetic parameter on the wave velocity and gas characteristics behind the wave is insignificant.

Keywords

• газодинаміка
• магнітне поле
• ударна хвиля
• рівняння характеристик
• метод Уізема
• співвідношення на розриві