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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.

We study the effects of dimensional confinement on the evolution of incompressible Rayleigh–Taylor mixing both in a bulk flow and in porous media by means of numerical simulations of the transport equations. In both cases, the confinement to two-dimensional flow accelerates the mixing process and increases the speed of the mixing layer. Dimensional confinement also produces stronger correlations between the density and the velocity fields affecting the efficiency of the mass transfer, quantified by the dependence of the Nusselt number on the Rayleigh number. This article is part of the theme issue ‘Scaling the turbulence edifice (part 2)’.

We report results from SAMI3/WACCM‐X simulations that small‐scale (∼ ${\\sim} $few 100 km) longitudinal variations in the meridional wind provide seeds to initiate equatorial plasma bubbles (EPBs). The meridional wind variations generate variations in the ion density along the magnetic field via ion‐neutral collisions. This in turn leads to longitudinal variations in the Pedersen conductivity and conductance producing localized E × ${\\times} $ B drifts that can initiate EPBs. The spatial dependence of the meridional wind variations can also determine the longitudinal spacing of EPBs.

Previous research on self-similar mixing caused by Rayleigh-Taylor (RT) instability is summarized and a recent series of high resolution large eddy simulations is described. Mesh sizes of approximately 2000 ×1000 × 1000 are used to investigate the properties of high Reynolds number self-similar RT mixing at a range of density ratios from 1.5 : 1 to 20 : 1. In some cases, mixing evolves from 'small random perturbations'. In other cases, random long wavelength perturbations (k−3 spectrum) are added to give self-similar mixing at an enhanced rate, more typical of that observed in experiments. The properties of the turbulent mixing zone (volume fraction distributions, turbulence kinetic energy, molecular mixing parameter, etc.) are related to the RT growth rate parameter, α. Comparisons are made with experimental data on the internal structure and the asymmetry of the mixing zone (spike distance/bubble distance). The main purpose of this series of simulations is to provide data for calibration of engineering models (e.g. Reynolds-averaged Navier-Stokes models). It is argued that the influence of initial conditions is likely to be significant in most applications and the implications of this for engineering modelling are discussed.

Three‐dimensional electromagnetic particle‐in‐cell simulations are used to investigate the stability properties of a plasma sheet equilibrium with a minimum in the magnetic normal (Bz) component. Such a configuration is found to be unstable to a ballooning/interchange type mode that is localized tailward of the Bz minimum. The mode has a relatively short dawn‐dusk wavelength of the order of the ion Larmor radius in the Bz field (∼2000 km) and a phase velocity in the direction of the ion diamagnetic drift with a magnitude about one‐fifth of the drift speed. The real frequency is about 60% of the midplane ion cyclotron frequency. The dominant mode polarization is δϕ and δB∥. A linear kinetic analysis including bounce and drift resonance interactions for the electrons and an orbit average over the flux tube volume for the Boltzmann term in the ion density perturbation produces agreement with the simulation mode properties and permits identification of the mode as the low‐frequency extension of the lower hybrid drift instability in straight magnetic geometry. In its nonlinear evolution, the mode develops Rayleigh‐Taylor fingers that extend across the Bz minimum and into the near‐Earth dipole region. These fingers transport magnetic flux earthward, and the flux is redistributed by electron Hall currents that flow around the fingers. This mode is likely to contribute to the nearly continuous presence of turbulence in the center of the plasma sheet.

Early studies on Rayleigh−Taylor instability (RTI) primarily relied on the Navier−Stokes (NS) model. As research progresses, it becomes increasingly evident that the kinetic information that the NS model failed to capture is of great value for identifying and even controlling the RTI process; simultaneously, the lack of analysis techniques for complex physical fields results in a significant waste of data information. In addition, early RTI studies mainly focused on the incompressible case and the weakly compressible case. In the case of strong compressibility, the density of the fluid from the upper layer (originally heavy fluid) may become smaller than that of the surrounding (originally light) fluid, thus invalidating the early method of distinguishing light and heavy fluids based on density. In this paper, tracer particles are incorporated into a single-fluid discrete Boltzmann method (DBM) model that considers the van der Waals potential. By using tracer particles to label the matter-particle sources, a careful study of the matter-mixing and energy-mixing processes of the RTI evolution is realized in the single-fluid framework. The effects of compressibility on the evolution of RTI are examined mainly through the analysis of bubble and spike velocities, the ratio of area occupied by heavy fluid, and various entropy generation rates of the system. It is demonstrated that: (i) compressibility has a suppressive effect on the spike velocity, and this suppressive impact diminishes as the Atwood number ( A t ) increases. The influence of compressibility on bubble velocity shows a staged behavior with increasing A t . (ii) The impact of compressibility on the entropy production rate associated with the heat flow ( S ˙ N O E F ) is related to the stages of RTI evolution. Moreover, this staged impact of compressibility on S ˙ N O E F varies with A t . Compressibility exhibits an inhibitory effect on the entropy production rate associated with viscous stresses ( S ˙ N O M F ). (iii) By incorporating the morphological parameter of the proportion of area occupied by heavy fluid ( A h ), it is observed that the first minimum point of d A h / d t can serve as a criterion for identifying the point at which bubble velocity reaches its first maximum value. The series of physical cognition provides a more accurate understanding of the RTI kinetics and a helpful reference for the development of corresponding regulation techniques.

The response of a thin film flowing under an inclined plane, modelled using the lubrication equation, is studied. The flow at the inlet is perturbed by the superimposition of a spanwise-periodic steady modulation and a decoupled temporally periodic but spatially homogeneous perturbation. As the consequence of the spanwise inlet forcing, the so-called rivulets grow downstream and eventually reach a streamwise-invariant state, modulated along the direction perpendicular to the flow. The linearized dynamics in the presence of a time-harmonic inlet forcing shows the emergence of a time-periodic flow characterized by drop-like structures (so-called lenses) that travel on the rivulet. The spatial evolution is rationalized by a weakly non-parallel stability analysis. The occurrence of the lenses, their spacing and thickness profile, is controlled by the inclination angle, flow rate, and the frequency and amplitude of the time-harmonic inlet forcing. The faithfulness of the linear analyses is verified by nonlinear simulations. The results of the linear simulations with inlet forcing are combined with the computations of nonlinear travelling lenses solutions in a double-periodic domain to obtain an estimate of the dripping length, for a large range of conditions.

The two-dimensional Rayleigh-Taylor instability problem is simulated with a multiple-relaxation-timediscrete Boltzmann model with a gravity term. Viscosity, heat conductivity, and Prandtl number ef-fects are probed from macroscopic and nonequilibrium viewpoints. In the macro sense, both viscosityand heat conduction show a significant inhibitory effect in the reacceleration stage, which is mainlyachieved by inhibiting the development of the Kelvin-Helmholtz instability. Before this, the Prandtlnumber effect is not sensitive. Viscosity, heat conductivity, and Prandtl number effects on nonequilib-rium manifestations and the degree of correlation between the nonuniformity and the nonequilibriumstrength in the complex flow are systematically investigated.

In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable and finally return to the unstable regime. We also exhibit numerical evidence of solutions with medium-sized norm of the derivative of the initial condition that develop a turning singularity.

The Rayleigh–Taylor (RT) instability occurs at an interface between two fluids of differing density during an acceleration. These instabilities can occur in very diverse settings, from inertial confinement fusion (ICF) implosions over spatial scales of ~10−3−10−1 cm (10–1,000 μm) to supernova explosions at spatial scales of ~1012 cm and larger. We describe experiments and techniques for reducing (“stabilizing”) RT growth in high-energy density (HED) settings on the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory. Three unique regimes of stabilization are described: (i) at an ablation front, (ii) behind a radiative shock, and (iii) due to material strength. For comparison, we also show results from nonstabilized “classical” RT instability evolution in HED regimes on the NIF. Examples from experiments on the NIF in each regime are given. These phenomena also occur in several astrophysical scenarios and planetary science [Drake R (2005) Plasma Phys Controlled Fusion 47:B419–B440; Dahl TW, Stevenson DJ (2010) Earth Planet Sci Lett 295:177–186].