Approximate Analytical Solution for Ionizing Cylindrical Magnetogasdynamic Shock Wave in Rotational Axisymmetric Self-Gravitating Perfect Gas: Isothermal Flow

Abstract

The propagation of ionizing cylindrical magnetogasdynamic shock wave in rotational axisymmetric self-gravitating perfect gas under isothermal flow condition is investigated. Mathematical model for the considered problem using system of PDEs is presented. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to power law with distance from the axis of symmetry in the undisturbed medium. The flow variables are expanded in power series and using that the zeroth and first order approximations are discussed. Solutions for zeroth order approximation are constructed in approximate analytical form. The effect of flow parameters namely: gravitational parameter $$G_{0}$$ , shock Cowling number $$C_{0}$$ , rotational parameter L and ambient density variation index q are studied on the flow variables and total energy of disturbance. Distribution of gasdynamical quantities are discussed. Radial fluid velocity and mass tends to zero near the axis of symmetry in general; but magnetic pressure, axial fluid velocity, non-dimensional components of vorticity vector $$l_{\theta }^{(0)}$$ and $$l_{z}^{(0)}$$ tend to positive infinity near the axis of symmetry. Azimuthal fluid velocity decreases as we move inwards from the shock to the axis of symmetry. Density and pressure vanish near the axis of symmetry thus forming a vacuum there. $$J_{0}$$ decreases with increase in value of ambient density variation index q or gravitational parameter $$G_{0}$$ ; whereas it increases with increase in value of rotational parameter L or shock Cowling number $$C_{0}$$ .