[en] We report non-linear solutions describing the large-scale coherent motion of bubbles and spikes in the Rayleigh-Taylor and Richtmyer-Meshkov instabilities for fluids with a finite density ratio in general three-dimensional case. The non-local character of the interface dynamics is taken into account with a multiple harmonic analysis. The theory yields a non-trivial dependence of the bubble velocity and curvature on the density ratio and reveals an important qualitative distinction between the dynamics of Rayleigh-Taylor and Richtmyer-Meshkov bubbles

[en] The stationary solutions of the Rayleigh-Taylor instability for spatially periodic flows with general symmetry are investigated here for the first time. The existence of a set of stationary solutions is established. The question of its dimensionality in function space is resolved on the basis of an analysis of the symmetry of the initial perturbation. The interrelationship between the dimensionality of the solution set and the symmetry of the flow is found. The dimensionality of the solution set is established for flows invariant with respect to one of five symmorphic two-dimensional groups. The nonuniversal character of the set of stationary solutions of the Rayleigh-Taylor instability is demonstrated. For flows in a tube, on the contrary, universality of the solution set, along with its independence of the symmetry of the initial perturbation, is assumed. The problem of the free boundary in the Rayleigh-Taylor instability is solved in the first two approximations, and their convergence is investigated. The dependence of the velocity and Fourier harmonics on the parameters of the problem is found. Possible symmetry violations of the flow are analyzed. Limits to previously studied cases are investigated, and their accuracy is established. Questions of the stability of the solutions obtained and the possibility of a physically correct statement of the problem are discussed

[en] We study the coherent motion of bubbles and spikes in the Richtmyer-Meshkov instability for isotropic three-dimensional and two-dimensional periodic flows. For equations governing the local dynamics of the bubble, we find a family of regular asymptotic solutions parametrized by the principal curvature at the bubble top. The physically significant solution in this family corresponds to a bubble with a flattened surface, not to a bubble with a finite curvature. The evolution of the bubble front is described and the diagnostic parameters are suggested

[en] We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position

[en] We propose a stochastic model to describe the random character of the dissipation process in Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for

[en] In this Introduction, we summarize and provide a perspective on 11 articles on 'Turbulent mixing and beyond'. The papers represent the broad variety of themes of the subject, and are concerned with fundamental aspects of turbulence, mixing and nonequilibrium dynamics. While each paper deals with a specific problem, the collection gives a panoramic overview of the subject at its present state of understanding. (authors)

[en] Turbulent mixing is a source of paradigm problems in physics, engineering and mathematics. Beyond this important interdisciplinary role, it has immense consequences for a broad range of applications in astrophysics, geophysics, climate and large-scale energy systems. In two volumes, we summarize and provide a perspective on the topic through some 20 articles focusing on turbulent mixing and beyond. The volumes are grouped, somewhat loosely, into those associated with fundamental aspects of turbulence and those specific to Rayleigh-Taylor turbulent mixing. (authors)

[en] This Introduction summarizes and provides a perspective on the papers representing one of the key themes of the 'Turbulent mixing and beyond' programme - the hydrodynamic instabilities of the Rayleigh - Taylor (RT) and Richtmyer - Meshkov (RM) type and their applications in nature and technology. The collection is intended to present the reader a balanced overview of the theoretical, experimental and numerical studies of the subject and to assess what is firm in our knowledge of the RT and RM turbulent mixing. (authors)