Experiments were conducted in the free-piston shock tube and shock tunnel with dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon to measure the transition condition in pseudosteady and steady flow. The transition condition in the steady flow, in which the wall was eliminated by symmetry, agrees with the calculated von Neumann condition. I n the real gases this calculation assumed thermodynamic equilibrium after the reflected shock. I n the pseudosteady flow of reflexion from a wedge the measured transition angle lies on the Mach-reflexion side of the calculated detachment condition by an amount which may be explained in terms of the displacement effect of the boundary layer on the wedge surface. A single criterion based on the availability of a length scale a t the reflexion point explains the difference between the pseudosteady and steady flow transition condition and predicts a hysteresis effect in the transition angle when the shock angle is varied during steady flow. No significant effects on the transition condition due to finite relaxation length could be detected. However, new experiments in which interesting relaxation effects should be evident are suggested.

It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

Previous work on the correlation of dissociative non-equilibrium effects on the flow field in front of blunt bodies considered the dependence of the dimensionless shock stand-off distance on the dimensionless dissociation rate immediately after the normal shock in the simple case of a diatomic gas with only one reaction. In this paper, the correlation is corrected to take into account the additional parameter of the dimensionless free-stream kinetic energy, and extended to the case of complex gas mixtures with many species and many reactions, by introducing a new reaction rate parameter that has a clear physical meaning, and leads to an approximate theory for the stand-off distance. Extensive new experimental results and numerical computations of air, nitrogen and carbon dioxide flow over spheres were obtained over a large range of total enthalpy. The results comprise surface heat flux measurements and differential interferograms. Both experimental results and numerical computations substantiate the approximate theory.

A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging velocimetry was applied to travelling hydraulic jumps giving centre-plane velocity field images at a frequency of 15 Hz over a Froude number range of 2-6. The mean vorticity determined from these images confirms the control-volume prediction to within the accuracy of the experiment. The flow field measurements show that a strong shear layer is formed at the toe of the wave, and extends almost horizontally downstream, separating from the free surface at the toe. Various vorticity generation mechanisms are discussed. IntroductionAt sufficiently high Froude number, the flow downstream of a hydraulic jump is so obviously rotational that it can be seen with the naked eye. The mechanism of vorticity generation is, however, still controversial. There is, of course, a source of vorticity at the solid boundary below the bottom fluid. The sign of the vorticity generated there depends on whether this boundary is stationary relative to the jump or relative to the upstream lower fluid. This vorticity stays within the boundary layer, however, and is not the concern here. In a recent publication, Yeh (1991) discusses mechanisms of vorticity generation in a steady-flow hydraulic jump. Three contributions are identified: viscous shear at the interface between the two fluids, the baroclinic torque brought about by the static pressure gradient in the upper fluid, and the baroclinic torque brought about by the dynamic pressure gradient associated with a suitable velocity field in the upper fluid. The last of these is shown to dominate the other two and is proportional to the density ratio. It requires the vertical component of the pressure gradient in the upper fluid to be of opposite sign to that corresponding to the static gradient, so that a significant velocity field with prescribed features has to be present in the upper fluid. Since this velocity field will depend on whether the far-field upper fluid is at rest relative to the wave or relative to the upstream lower fluid, the vorticity generation would be different in these two cases.When the density ratio is very large, such as for an air/water interface, where it is approximately 1000, such a dependence on the motion of the tenuous upper fluid seems too sensitive. One might carry the argument to the extreme case of a t Permanent address:

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