Snezhana I. Abarzhi

Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing

We review the theoretical developments in the field of Rayleigh–Taylor instabilities and turbulent mixing, discuss what is known and what is not known about the phenomenon, and outline the features of similarity of the turbulent mixing process. Based on the physical intuition and on the results of rigorous theoretical studies, we put forward some new ideas on how to grasp the essentials of the mixing process and consider the influence of momentum transport on the invariants and on scaling and statistical properties of the unsteady turbulent mixing.

Stability of a hydrodynamic discontinuity

While looking from a far field at a discontinuous front separating incompressible ideal fluids of different densities, we identify two qualitatively different behaviors of the front—unstable and stable—depending upon whether the energy flux produced by the perturbed front is large or small compared to the flux of kinetic energy across the planar front. Landaus solution for the Landau–Darrieus instability is consistent with one of these cases.

On fundamentals of Rayleigh-Taylor turbulent mixing

We analyze symmetries, invariants, scaling and spectra of turbulent mixing induced by the Rayleigh-Taylor instability. The properties of this unsteady, anisotropic, and inhomogeneous turbulent process are found to depart from canonical Kolmogorov scenario. Time- and scale-invariance of the rate of momentum loss leads to non-dissipative momentum transfer between the scales, to 1/2 and 3/2 power-law scale dependencies of the velocity and Reynolds number respectively, and to spectra distinct from Kolmogorov. Turbulent mixing exhibits more order compared to isotropic turbulence, and its viscous and dissipation scales are set by the flow acceleration.

Tendency of spherically imploding plasma liners formed by merging plasma jets to evolve toward spherical symmetry

We have performed three-dimensional (3D) simulations using smoothed particle hydrodynamics (SPH) in order to study the effects of discrete plasma jets on the processes of plasma liner formation, implosion on vacuum, and expansion. It was found that the pressure histories of the inner portion of the liner from 3D SPH simulations with a uniform liner and with 30 discrete plasma jets were qualitatively and quantitatively similar from peak compression through the complete stagnation of the liner. The 3D simulations with a uniform liner were first benchmarked against results from one-dimensional radiation-hydrodynamic simulations [T. J. Awe et al., Phys. Plasmas 18, 072705 (2011)]. Two-dimensional plots of the pressure field show that the discrete jet SPH case evolves towards a profile that is almost indistinguishable from the SPH case with a uniform liner, thus indicating that non-uniformities due to discrete jets are smeared out by late stages of the implosion. The processes of plasma liner formation and implosion on vacuum were shown to be robust against Rayleigh-Taylor instability growth. Finally, interparticle mixing for a liner imploding on vacuum was investigated. The mixing rate was found to be very small until after the peak compression for the 30 jet simulations.

A comparative study of approaches for modeling Rayleigh–Taylor turbulent mixing

This paper considers similarities and differences in the governing mechanisms and basic properties of Rayleigh?Taylor turbulent mixing as discussed in recent theoretical and heuristic modeling studies and briefly discusses how these mechanisms and properties may be explored in experiments and simulations. We were motivated by a number of stimulating questions, thoughtful comments and sagacious remarks by our colleagues and the anonymous referees, whose contribution to improving this work is warmly appreciated.

Review of nonlinear dynamics of the unstable fluid interface: conservation laws and group theory

In this paper, we briefly overview some theoretical approaches and empirical modeling approaches of the nonlinear Rayleigh?Taylor instabilities, which have been developed over recent decades, summarize the results of the group theory analysis of the nonlinear coherent dynamics in Rayleigh?Taylor and Richtmyer?Meshkov flows, consider the issues of validation and verification of the theories and models, and outline some criteria for the estimate of the fidelity and information capacity of the experimental and numerical data sets.

What is certain and what is not so certain in our knowledge of Rayleigh–Taylor mixing?

Past decades significantly advanced our understanding of Rayleigh–Taylor (RT) mixing. We briefly review recent theoretical results and numerical modelling approaches and compare them with state-of-the-art experiments focusing the readers attention on qualitative properties of RT mixing.

Turbulent mixing and beyond

Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high- and low-energy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free—subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.

Scale coupling in Richtmyer-Meshkov flows induced by strong shocks

We perform the first systematic study of the nonlinear evolution and scale coupling in Richtmyer-Meshkov (RM) flows induced by strong shocks. The smoothed particle hydrodynamics code (SPHC) is employed to ensure accurate shock capturing, interface tracking and accounting for the dissipation processes. We find that in strong-shock-driven RMI the background motion is supersonic. The amplitude of the initial perturbation strongly influences the flow evolution and the interfacial mixing that can be sub-sonic or supersonic. At late times the flow remains laminar rather than turbulent, and RM bubbles flatten and decelerate. In the fluid bulk, reverse cumulative jets appear and “hot spots” are formed—local heterogeneous microstructures with temperature substantially higher than that in the ambient. Our numerical simulations agree with the zero-order, linear, weakly nonlinear, and highly nonlinear theoretical analyses as well as with the experiments and suggest that the evolution of RMI is a multi-scale and heter...

Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II

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.