Transonic shock and supersonic shock in the regular reflection of a planar shock

Abstract.

We study the regular reflection problem of a planar shock. The criterion of regular reflection of a planar shock for polytropic gases is given, which is the expression of critical angle of incidence $\alpha_e < \alpha_0 = {\rm arcot}\left(\frac{1}{1-\mu^2}\frac{\rho_0}{\rho_1}\left(1-\frac{\rho_0}{\rho_1}\right)\right)^{1/2}$, where ρ₀ and ρ₁ are the density of the gas in the front and back of the incident shock respectively. The expression of sonic angle α _s (> α _e ) is also given. When the angle of incidence is greater than or equal to the sonic angle α _s , the reflected shock is a transonic shock, otherwise, it is a supersonic shock.