Determination of gradients of flow variables behind three-dimensional stationary and pseudo stationary curved shock waves in conducting gases

Abstract

In this paper we have obtained the gradients of magnetic field, velocity, pressure and density behind a shock wave in three dimensional steady motion of a conducting gas. For the shock configuration, we take a continuous differentiable function of coordinates and it is assumed that the components of the magnetic field Hⁱ , velocity components uⁱ, pressure p and density ρ behind the shock-surface are differentiable functions. Moreover we take Hⁱ, uⁱ, p and ρ in front of the shock-wave as constant quantities. In § 4 we have obtained the gradients of flow and field quantities behind the pseudostationary shockwave. § 5 is devoted to the calculation of gradients of flow and field quantities in cases where the normal component of the magnetic field is zero on both sides of the shock wave. In § 6 the relation between the curvature k of the shock-surface and the curvature K of the stream line just behind the shock surface in two dimensional steady motion has been derived. § 7 deals with the determination of the ratio K/k for an attached shock in the case of a wedge.