to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

The interaction of a planar shock wave with a polygonal N2 volume surrounded by SF6 is investigated experimentally and numerically. Three polygonal interfaces (square, triangle and diamond) are formed by the soap film technique developed in our previous work, in which thin pins are introduced as angular vertexes to connect adjacent sides of polygonal soap films. The evolutions of the shock-accelerated polygonal interfaces are then visualized by a high-speed schlieren system. Wave systems and interface structures can be clearly identified in experimental schlieren images, and agree well with the numerical ones. Quantitatively, the movement of the distorted interface, and the length and height of the interface structures are further compared and good agreements are achieved between experimental and numerical results. It is found that the evolution of these polygonal interfaces is closely related to their initial shapes. In the square interface, two vortices are generated shortly after the shock impact around the left corner and dominate the flow field at late stages. In the triangular and diamond cases, the most remarkable feature is the small ‘SF6 jet’ which grows constantly with time and penetrates the downstream boundary of the interface, forming two independent vortices. These distinct morphologies of the three polygonal interfaces also lead to the different behaviours of the interface features including the length and height. It is also found that the velocities of the vortex pair predicted from the theory of Rudinger and Somers (J. Fluid Mech., vol. 7, 1960, pp. 161‐176) agree with the experimental ones, especially for the square case. Typical free precursor irregular refraction phenomena and the transitions among them are observed and analysed, which gives direct experimental evidence for wave patterns and their transitions at a slow/fast interface. The velocities of triple points and shocks are experimentally measured. It is found that the transmitted shock near the interface boundary has weakened into an evanescent wave.

/pdf/on-the-interaction-of-a-planar-shock-with-a-light-polygonal-54wu3sewf7.pdf

On the interaction of a planar shock with a light polygonal interface

The interaction of a planar shock wave ( ) with an polygonal inhomogeneity surrounded by air is experimentally investigated. Six polygons including a square, two types of rectangle, two types of triangle, and a diamond are generated by the soap film technique developed in our previous work, in which thin pins are used as angular vertexes to avoid the pressure singularities caused by the surface tension. The evolutions of the shock-accelerated polygons are captured by a high-speed schlieren system from which wave systems and the interface characteristics can be clearly identified. Both regular and irregular refraction phenomena are observed outside the volume, and more complex wave patterns, including transmitted shock, refracted shock, Mach stem and the interactions between them, are found inside the volume. Two typical irregular refraction phenomena (free precursor refraction, FPR, and free precursor von Neumann refraction, FNR) are observed and analysed, and the transition from FPR to FNR is found, providing the experimental evidence for the transition between different wave patterns numerically found in the literature. Combined with our previous work (Zhai et al., J. Fluid Mech., vol. 757, 2014, pp. 800–816), the reciprocal transitions between FPR and FNR are experimentally confirmed. The velocities and trajectories of the triple points are further measured and it is found that the motions of the triple points are self-similar or pseudo-stationary. Besides the shock dynamics phenomena, the evolutions of these shocked heavy polygonal volumes, which are quite different from the light ones, are captured and found to be closely related to their initial shapes. Specifically, for square and rectangular geometries, the different width–height ratios result in different behaviours of shock–shock interaction inside the volume, and subsequently different features for the outward jet and the interface. Quantitatively, the time-variations of the interface scales, such as the width and the normalized displacements of the edges, are obtained and compared with those from previous work. The comparison illustrates the superiority of the interface formation method and the significant effect of the initial interface shape on the interface features. Furthermore, the characteristics of the vortex core, including the velocity and vortex spacing, are experimentally measured, and the vortex velocity is compared with those from some circulation models to check the validity of the models. The results in the present work enrich understanding of the shock refraction phenomenon and the database of research into Richtmyer–Meshkov instability (RMI).

/pdf/on-the-interaction-of-a-planar-shock-with-an-polygon-3wdtvgtfpn.pdf

On the interaction of a planar shock with an polygon

Richtmyer–Meshkov (RM) instability is regarded as a central role for understanding the hydrodynamic processes involved in inertial confinement fusion, supersonic combustion and supernova explosion....

https://journals.sagepub.com/doi/pdf/10.1177/0954406217727305

Review of experimental Richtmyer–Meshkov instability in shock tube: From simple to complex:

A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M0=1.2 and a converging angle of 15° is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.

Generation of cylindrical converging shock waves based on shock dynamics theory

In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ0, the incident planar shock Mach number M0, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M0 and h and moderate θ0. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of ...

Parametric study of cylindrical converging shock waves generated based on shock dynamics theory

The evolution of an elliptic heavy-gas (SF6) cylinder accelerated by a planar weak shock wave is investigated experimentally using particle imagevelocimetry(PIV) diagnostics, and the emphasis is on the aspect ratio effect on shock-elliptic cylinder interaction. Experiments are conducted at five different aspect ratios (the ratio of length in streamwise and spanwise directions) varied from 0.25 to 4.0. PIV raw images and quantitative flow field data are obtained at t = 0.6 ms after the shock impact. As the aspect ratio increases, the interface morphology develops faster owing to more vorticity produced along the interface and smaller vortex spacing between the two vortex cores. For each case in this study, the maximal fluctuating velocity locates at the middle point of the two counter-vortices. The histograms of fluctuating velocity reveal that a distinct double-peak structure appears in the largest aspect ratio case in comparison with a single-peak structure in the smallest aspect ratio case. The vortex velocities predicted by the theoretical model [G. Rudinger and L. M. Somers, “Behaviour of small regions of different gases carried in accelerated gas flows,” J. Fluid Mech. 7, 161–176 (1960)] agree well with the experimental ones. With the increase of aspect ratio, the maximal value of vorticity increases as well as the circulation, and more low-magnitude quantities are generated, which indicates the formation of multi-scale flow structure in the late mixing process. It is found that the experimental circulation of the vortex motion is reasonably estimated by the ideal point vortex-pair model.

Aspect ratio effect on shock-accelerated elliptic gas cylinders

The interaction of a planar shock with one elliptic heavy-gas (SF6) cylinder surrounded by air is investigated experimentally. By changing the aspect ratio of the elliptic cylinder, the influence of the initial shape on the evolution of the interface is visualized by a series of dynamic photos utilized by a high-speed camera. It is found that the longer the axis perpendicular to the shock front, the faster and the severer the deformation of the gas cylinder. This can be explained mainly by the different amount of vorticity produced by the misalignment between the density gradient and the pressure gradient. When the vertical axis is much longer than the horizontal axis, the vorticity production is mainly concentrated at the upper and lower corners, which rolls up in time, and results in a structure of big vortex-pair. When the horizontal axis is much longer than the vertical axis, the baroclinic vorticity production distributes at almost every position along the interface, which leads to a faster rolling up of vortices, and even second vortex may develop at later times.

On interaction of shock wave with elliptic gas cylinder

We studied the evolution of elliptic heavy SF6 gas cylinder surrounded by air when accelerated by a planar Mach 1.25 shock. A multiple dynamics imaging technology has been used to obtain one image of the experimental initial conditions and five images of the time evolution of elliptic cylinder. We compared the width and height of the circular and two kinds of elliptic gas cylinders and analyzed the vortex strength of the elliptic ones. Simulations are in very good agreement with the experiments, but due to the different initial gas cylinder shapes, a certain difference of the initial density peak and distribution exists between the circular and elliptic gas cylinders, and the latter initial state is more sensitive and more inenarrable.

Cangli Liu

Papers

Generation of cylindrical converging shock waves based on shock dynamics theory

Parametric study of cylindrical converging shock waves generated based on shock dynamics theory

Aspect ratio effect on shock-accelerated elliptic gas cylinders

On interaction of shock wave with elliptic gas cylinder

Experimental and numerical study of shock-accelerated elliptic heavy gas cylinders