The interaction of two conical shock waves, one converging and straight and the other diverging and curvilinear, in an axisymmetric flow was investigated both experimentally and numerically. A double-loop hysteresis was discovered in the course of the experimental investigation. The double-loop hysteresis consisted of a major one, associated with the interaction between the boundary layer and the wave configuration, and a minor one, associated with the dual-solution phenomenon, which is known to be non-viscous-dependent. The minor hysteresis loop was found to be an internal hysteresis loop of the major one. As expected the numerical Euler calculations failed to detect the viscous-dependent major hysteresis loop but did succeed in obtaining the non-viscous-dependent minor (internal) hysteresis loop. In addition, multiple hysteresis loops, associated with the interaction between the shock wave configuration and the edge of the curvilinear mobile cone were also observed. The non-viscous minor hysteresis loop involved different overall shock wave reflection configurations, and the other hysteresis loops involved the same shock wave reflection configuration but different flow patterns.

The effect of the downstream pressure (defined here as the wake pressure behind the tail of the reflecting wedge) on shock wave reflection in steady flows is investigated both numerically and analytically. The dependence of the shock wave configurations on the downstream pressure is studied. In addition to the incident-shock-waveangle-induced hysteresis, which was discovered a few years ago, a new downstreampressure-induced hysteresis has been found to exist. The numerical study reveals that when the downstream pressure is sufficiently high, an inverse-Mach reflection wave configuration, which has so far been observed only in unsteady flows, can be also established in steady flows. Very good agreement between the analytical predictions and the numerical results is found.

A flow-Mach-number-induced hysteresis phenomenon, in the shock-on-shock interaction of conical shock waves, is investigated numerically, by solving the Euler equations, using a W-modification of the non-stationary Godunov method with second-order accuracy both in space and time. The investigation reveals a multi-path hysteresis loop. It is shown that there are flow Mach number ranges in which three different wave configurations can be obtained for identical flow conditions. This study complements an earlier study by Ben-Dor et al. (2001) in which an angle-ofincidence-induced hysteresis was investigated both numerically and experimentally over a similar geometry. Based on the experimental findings of Ben-Dor et al.'s (2001) study, it is hypothesized that, in fact, four different wave configurations, three inviscid and one viscous, can be obtained for identical flow conditions. Since the geometry under investigation resembles supersonic intakes, this finding is relevant to their performance in supersonic/hypersonic flight.

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The regular ↔ Mach reflection transition in steady flows was investigated numerically using the W-modified Godunov's scheme. In addition to the incident-shock-wave-angle-induced hysteresis, which was discovered a few years ago and reconfirmed in the present study, a new downstream-pressure-induced hysteresis was found to exist.