Regular and Mach reflection of shock waves

Abstract

The properties that distinguish a shock wave from other waves are that its thickness is negligible compared with other characteristic lengths, and that the state of the medium is changed irreversibly by the passage of the wave. Shocks are therefore a highly nonlinear phenomenon, and parameter changes may be expected to lead to numerous bifurcations. The multitude of possibilities is compounded when more than one shock occurs, such as in the interaction of a shock with a solid surface or symmetry plane (i.e. in shock reflection). The subject of shock reflection is so complicated that it is necessary to introduce it at some length. In the interest of conciseness, this is done according to a logical rather than a historical sequence, with explicit reference to the important authors omitted in the text unless their work is relatively recent. Salient points in the early development of the subject should be mentioned here, however. These may be found in the experiments of Mach (1878), the theoretical work of von Neumann(1943), the experimental and theoretical work of the group around Bleakney at Princeton (e.g. Bleakney & Taub 1949, Smith 1945), the experiments of Kawamura & Saito (1956), Smith (1959), and Bryson & Gross (1961), and the theoretical work Lighthill (1949) and Jones et al. (195l). A review by Pack (1964) gives detailed references. Of the work since 1960, that of the group around Glass at Toronto (e.g. Law & Glass 1971, Ben-Dor & Glass 1979, 1980) and around Henderson at Sydney (e.g. Henderson & Lozzi 1975, 1979, Henderson & Gray 1981) stand out. A review by Griffith (1981) gives more detailed references. In this review the discussion is restricted to plane flow. This is because relatively little work has been done on three-dimensional situations, and because a compromise had to be made between depth and breadth of the field covered.