A new, more accurate prediction of Mach stem height in steady flow is presented. In addition, starting with a regular reflection in the dual-solution domain, the growth rate of the Mach stem from the time it is first formed till it reaches its steady-state height is presented. Comparisons between theory, experiments, and computations are presented for the Mach stem height. The theory for the Mach stem growth rate in both two and three dimensions is compared to computational results. The Mach stem growth theory provides an explanation for why, once formed, a Mach stem is relatively persistent. Nomenclature g = spacing between wedge and axis of symmetry M = Mach number P = pressure s = Mach stem height U = speed w = wedge length = leading shock angle with respect to the freestream = ratio of specific heats = triple-point slip-line angle = wedge angle with respect to the freestream = Mach angle = density = triple-point reflected shock angle Subscripts a = conditions directly behind Mach stem Ms = Mach stem properties tp = triple-point properties 1 = region 1 condition 2 = region 2 condition 3 = conditions between Mach stem and sonic throat ? = sonic throat condition 1 = freestream condition Superscripts tp = triple-point reference frame = nondimensional quantity

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A study of the mechanism by which disturbances can cause tripping between steady-flow regular and Mach reflection in the dual-solution domain is presented. Computational results indicate that the disturbance shock created as a result of the impact of dense particles on one of the shock-generating wedges can cause transition from regular to Mach reflection. The disturbance shock may also be generated by direct energy deposition on the wedge. Estimates of the lower bound of the required energy for transition to occur are presented and compared to values obtained computationally. Experiments were performed at Mach 4.0 in a Ludwieg tube that has a test duration of 100 ms. Proper starting of the flow necessitated operation with an upstream diaphragm and modifications in the dump tank. The reflection state was changed by rapid rotation of one of the shock-generating wedges. The flow in the facility is sufficiently quiet to permit entering the dual-solution domain to approximately its midpoint before spontaneous transition to the Mach reflection occurs. The short test time prompted a study of the effect of wedge rotation speed on the transition from regular to Mach reflection. Transition due to deposition of energy on one of the wedges was also examined by using a pulsed laser focused on one of the two wedges. Measurements of the minimum energy to bring about transition and of the rapid growth of the Mach stem to its steady-state are compared to numerical and theoretical predictions.

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The problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest is studied without the use of the strong-shock approximation. Dimensional arguments are first used to show that this flow admits a general solution where an infinitesimally weak shock from infinity strengthens as it converges towards the origin. For a perfect-gas equation of state, this solution depends only on the dimensionality of the flow and on the ratio of specific heats. The Guderley power-law result can then be interpreted as the leading-order, strong-shock approximation, valid near the origin at the implosion centre. We improve the Guderley solution by adding two further terms in the series expansion solution for both the incoming and the reflected shock waves. A series expansion, valid where the shock is still weak and very far from the origin, is also constructed. With an appropriate change of variables and using the exact shock-jump conditions, a numerical, characteristics-based solution is obtained describing the general shock motion from almost infinity to very close to the reflection point. Comparisons are made between the series expansions, the characteristics solution, and the results obtained using an Euler solver. These show that the addition of two terms to the Guderley solution significantly extends the range of validity of the strong-shock series expansion.