Supernovae and their remnants are a central problem in astrophysics due to their role in the stellar evolution and nuclear synthesis. A supernova’s explosion is driven by a blast wave causing the development of Rayleigh–Taylor and Richtmyer–Meshkov instabilities and leading to intensive interfacial mixing of materials of a progenitor star. Rayleigh–Taylor and Richtmyer–Meshkov mixing breaks spherical symmetry of a star and provides conditions for synthesis of heavy mass elements in addition to light mass elements synthesized in the star before its explosion. By focusing on hydrodynamic aspects of the problem, we apply group theory analysis to identify the properties of Rayleigh–Taylor and Richtmyer–Meshkov dynamics with variable acceleration, discover subdiffusive character of the blast wave-induced interfacial mixing, and reveal the mechanism of energy accumulation and transport at small scales in supernovae.

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 reader's attention on qualitative properties of RT mixing.

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 heterogeneous process with a complicated character of scale coupling.

While it is a common wisdom that initial conditions influence the evolution of the Richtmyer-Meshkov instability (RMI), the research in this area is focused primarily on the effects of the wavelength and amplitude of the interface perturbation. The information has hitherto largely ignored the influences on RMI dynamics of the relative phase of waves constituting a multiwave initial perturbation and the interference of the perturbation waves. In this work we systematically study the influence of the relative phase and the interference of waves constituting a multiwave initial perturbation on a strong-shock-driven Richtmyer-Meshkov unstable interface separating ideal fluids with contrast densities. We apply group theory analysis and smoothed particle hydrodynamics numerical simulations. For verification and validation of the simulations, qualitative and quantitative comparisons are performed with rigorous zeroth-order, linear, and nonlinear theories as well as with gas dynamics experiments achieving good agreement. For a sample case of a two-wave (two-mode) initial perturbation we select the first-wave amplitude enabling the maximum initial growth rate of the RMI and we vary the second-wave amplitude from 1% to 100% of the first-wave amplitude. We also vary the relative phase of the first and second waves and consider the in-phase, the antiphase and the random-phase cases. We find that the relative phase and the interference of waves are important factors of RMI dynamics influencing qualitatively and quantitatively the symmetry, morphology, and growth rate of the Richtmyer-Meshkov unstable interface, as well as the order and disorder in strong-shock-driven RMI.

We focus on the classical problem of the dependence on the initial conditions of the initial growth-rate of strong shock driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics simulations to describe the simulation data with statistical confidence in a broad parameter regime. For the given values of the shock strength, fluid density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of the RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data.