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In 1942 Guderley investigated the behaviour of the typical parameters near the axis when he was studying the focusing of cylindrical shock waves by solving the partial differential equations using the similarity method. He pre­ dicted an infinitely large pressure and temperature at the axis of convergence. Since then many theoretical and experimental studies have been performed on shock focusing as an energy source for the generation of very high pressures and temperatures. Many experimental investigations confirmed the idea of Guderley that at the centre of convergence extremely high pressures and temperatures can be obtained. At the Technical University of Darmstadt we performed a numerical exper­ iment to investigate the shock-focusing phenomenon, and many test problems were solved using the Rusanov scheme. At the centre of convergence we ob­ tained extremely high pressures and temperatures. The results of these inves­ tigations were compared with the experimental work done at the Max Planck Institute for Fluid Dynamics Research in Gottingen. The three-dimensional time-dependent shock wave which was created by a centred gas volume under high pressure interacts with the plane walls of the cavity and leads to a focusing effect after the explosion. The symmetry-preserving character of the invari­ ant difference scheme under use was proved numerically by calculation over a long interval of time. A test run of our investigation was also made at the Institute of Computational Fluid Dynamics in Tokyo, Japan.

Free surface flows arise in the natural world, physical and biological sciences and in some areas of modern technology and engineering. Exam­ ples include the breaking of sea waves on a harbour wall, the transport of sloshing fluids in partly filled containers, and the design of micronozzles for high speed ink-jet printing. Apart from the intrinsic mathematical challenge in describing and solving the governing equations, there are usually important environmental, safety and engineering features which need to be analysed and controlled. A rich variety of techniques has been developed over the past two decades to facilitate this analysis; singular perturbations, dynamical systems, and the development of sophisticated numerical codes. The extreme and sometimes violent nature of some free surface flows taxes these methods to the limit. The work presented at the symposium addressed these limits and can be loosely classified into four areas: (i) Axisymmetric free surface flows. There are a variety of problems in the printing, glass, fertiliser and fine chemical industries in which threads of fluid are made and controlled. Presentations were made in the areas of pinch-off for inviscid and viscous threads of fluid, recoil effects after droplet formation and the control of instability by forced vibration. (ii) Dynamic wetting. The motion of three phase contact lines, which are formed at the junction between two fluids and a solid, plays an important role in fluid mechanics.

Advances in Turbulence VII contains an overview of the state of turbulence research with some bias towards work done in Europe. It represents an almost complete collection of the invited and contributed papers delivered at the Seventh European Turbulence Conference, sponsored by EUROMECH and ERCOFTAC and organized by the Observatoire de la Côte d'Azur. New high-Reynolds number experiments combined with new techniques of imaging, non-intrusive probing, processing and simulation provide high-quality data which put significant constraints on possible theories. For the first time, it has been shown, for a class of passive scalar problems, why dimensional analysis sometimes gives the wrong answers and how anomalous intermittency corrections can be calculated from first principles. The volume is thus geared towards specialists in the area of flow turbulence who could not attend the conference as well as anybody interested in this rapidly moving field.