A simple physical theory of weak Mach reflection over plane surfaces

Abstract.

It is shown that simple physical principles coupled with the inviscid shock jump relations can be applied to the problem of weak Mach reflection to the extent that the triple point path can be predicted from the incident shock Mach number $M_{\rm i}$, gas specific heat ratio $\gamma$ and the inclination angle $\theta_{\rm w}$ of the reflecting surface to the shock normal. Comparison with the Euler code data and with experiments show close agreement for conditions both far and close to transition and that the general shape of the reflected and Mach stem shocks follow simple curves except in the neighbourhood of the triple point. The conflict at the triple point in matching the flow deflection angles and pressures across the contact discontinuity remains. It is shown however that the simple model presented here gives a close match to the cfd and experimental overall shock and contact surface shapes although it cannot predict these or the flow properties in any detail.