Laser-induced three-dimensional (3D) Richtmyer–Meshkov and Rayleigh–Taylor instabilities (RMI and RTI) on metal target in the semi-confined configuration (SCC) show the new paradigm of wave-vortex mixing. The SCC enables extended lifetime of a hot vapor/plasma plume above the target surface and the formation of fast multiple reshocks. This causes – in the central region (CR) of Gaussian-like spot – the evolution of RMI with the spike breakup (Lugomer, 2016b), while in the near CR causes the RMI followed by the RTI. The density interface is transformed into the large-scale broken irregular, quasi-periodic web, which comprises the RTI mushroom-shape spikes and the coherent wave-vortex structures such as the line solitons and vortex filaments. The intensity and direction of reshocks change (due to irregularity of the interface) and cause the formation of domains with the weak and the strong reshocks effects. The weak reshocks affect mushroom-shape spikes only slightly, while the strong ones cause their deformation and symmetry break, bubble collapse, and separation of the horizontal flow into vortex ribbons. Interaction of ribbons with spikes and bubbles causes the ribbon pinning, looping, winding, and formation of knotted and tangled structures. The line solitons, vortex filaments, and ribbons tend to organize into complex large-scale structures with the low wave-vortex turbulent mixing. They represent the new paradigm of 3D RMI and RTI in which the transition to the small-scale turbulent mixing does not appear.

In this experimental study, the ablative Richtmyer–Meshkov (RM) and the Rayleigh–Taylor (RT) instabilities were generated by the laser pulse of Gaussian-like power profile. The initial multi-modal perturbation, the inhomogeneous momentum transfer and different Atwood numbers generate different shapes of spikes and bubbles in the central region (CR) and the near-central region (NCR) of the spot. A one-dimensional Gaussian-like power profile causes the formation of the wavy-like rows of aperiodic spikes. The periodic spike segments inside the rows appear due to locally coherent flow. In the NCR, the mushroom-shape spikes tend to the organization on the isotropic square and the anisotropic rhombic lattices. The increase of the lattice periods two, three, or four times indicates formation of superstructures. The growth of sharp asymmetric RM/RT spikes in the CR is fast, uncorrelated and linear, while the growth of the symmetric mushroom-shape ones in the NCR is slow, correlated, and nonlinear.

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

Afin d'étudier la structure fine de la turbulence pariétale en présence de variations importantes de densité, une analyse statistique des données expérimentales, dans une soufflerie à recirculation, est effectuée. Les résultats montrent que la relaxation du facteur de dissymétrie de $u'(S_{u'}$) s'effectue plus rapidement dans la couche externe que près de la paroi, aussi bien pour l'injection de l'air que pour l'injection d'hélium. $S_{u'}$ croît près de la fente d'injection de façon appréciable et cette augmentation est nettement plus accentuée pour l'injection de l'air que l'injection d'hélium. Cette croissance du facteur de dissymétrie près de la fente d'injection peut s'expliquer par l'augmentation du flux convectif longitudinal de l'énergie turbulente dans cette zone. Les résultats montrent, pour la distribution du facteur d'aplatissement $F_{u'}$, qu'il n'y a pas d'effet important du gradient de densité sur la structure intermittente de la vitesse longitudinale instantanée dans la zone développée, $x/\delta \ge 5$. L'analyse statistique menée dans cette étude montre que l'injection d'hélium, dans la couche limite, engendre des éjections plus violentes que dans le cas d'une injection d'air. Ce résultat est confirmé par la contribution importante des éjections au flux massique turbulent.

This paper discusses two-terminal series-parallel networks occurring in Applied Probability and other contexts where the mathematical theory of reliability is developed. Eighty years ago Mac Mahon successfully discussed the number of different structures built of n identical components [1]; later Knödel [3] and Carlitz and Riordan [4] in the 1950's investigated the number of different structures built of n different components. However, in many new applications, engineers and statisticians have to study structures having n components with a specification defining various types of components and stating how many identical components of each kind should be used. This general problem is investigated in Section 7 whilst in Sections 1–6 results obtained earlier are presented and it is shown there how modern approaches to combinatorics (particularly Pólya's Enumerative Combinatorial Analysis) can simplify some reasoning of previous authors.