Interaction of Linear Waves with Oblique Shock Waves

Abstract

Formulas are derived for the amplitudes of waves that diverge from a shock as a result of any given incident disturbance. For strong shocks, that is the Mach number (M) is large, in an ideal gas it is shown that the pressure amplitude and the component of the energy flux normal to the shock of a transmitted sound wave are of O (M2 greater than those in the incident sound wave. Furthermore, if the impinging sound wave is incident near the critical angle the ratio of the pressure amplitude of the transmitted sound wave to that of the incident one is of O (M3). On the other hand, if a sound wave is normally incident upon the back of the shock, only about 1% of the acoustic energy flux is reflected in the form of sound waves. It is also shown that incident entropy-vorticity waves can generate intense sound waves behind a strong shock. The dependence of the transmission, reflection, and generation coefficients for sound waves on the Mach number and the angle of incidence is depicted in a series of graphs. The results are applied to the amplification of small disturbances in the solar wind on passage through the bow shock of the earth.