A Turbulent Heliosheath Driven by the Rayleigh–Taylor Instability

The heliosphere is the bubble formed by the solar wind as it interacts with the interstellar medium (ISM). The collimation of the heliosheath (HS) flows by the solar magnetic field in the heliotail into distinct north and south columns (jets) is seen in recent global simulations of the heliosphere. However, there is disagreement between the models about how far downtail the two-lobe feature persists and whether the ambient ISM penetrates into the region between the two lobes. Magnetohydrodynamic simulations show that these heliospheric jets become unstable as they move down the heliotail and drive large-scale turbulence. However, the mechanism that produces this turbulence had not been identified. Here we show that the driver of the turbulence is the Rayleigh–Taylor (RT) instability produced by the interaction of neutral H atoms streaming from the ISM with the ionized matter in the HS. The drag between the neutral and ionized matter acts as an effective gravity, which causes an RT instability to develop along the axis of the HS magnetic field. A density gradient exists perpendicular to this axis due to the confinement of the solar wind by the solar magnetic field. The characteristic timescale of the instability depends on the neutral H density in the ISM and for typical values the growth rate is ∼3 years. The instability destroys the coherence of the heliospheric jets and magnetic reconnection ensues, allowing ISM material to penetrate the heliospheric tail. Signatures of this instability should be observable in Energetic Neutral Atom maps from future missions such as the Interstellar Mapping and Acceleration Probe (IMAP). The turbulence driven by the instability is macroscopic and potentially has important implications for particle acceleration.

On instability of Rayleigh–Taylor problem for incompressible liquid crystals under $L^{1}$-norm

We investigate the nonlinear Rayleigh–Taylor (RT) instability of a nonhomogeneous incompressible nematic liquid crystal in the presence of a uniform gravitational field. We first analyze the linearized equations around the steady state solution. Thus we construct solutions of the linearized problem that grow in time in the Sobolev space $H^{4}$ H 4 , then we show that the RT equilibrium state is linearly unstable. With the help of the established unstable solutions of the linearized problem and error estimates between the linear and nonlinear solutions, we establish the nonlinear instability of the density, the horizontal and vertical velocities under $L^{1}$ L 1 -norm.

A new upper bound for the largest growth rate of linear Rayleigh–Taylor instability

We investigate the effect of (interface) surface tensor on the linear Rayleigh–Taylor (RT) instability in stratified incompressible viscous fluids. The existence of linear RT instability solutions with largest growth rate Λ is proved under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold $\vartheta _{\mathrm{c}}$ ϑ c ) by the modified variational method of PDEs. Moreover, we find a new upper bound for Λ. In particular, we directly observe from the upper bound that Λ decreasingly converges to zero as ϑ goes from zero to the threshold $\vartheta _{\mathrm{c}}$ ϑ c .

A Turbulent Heliosheath Driven by Rayleigh Taylor Instability

The heliosphere is the bubble formed by the solar wind as it interacts with the interstellar medium (ISM). Studies show that the solar magnetic field funnels the heliosheath solar wind (the shocked solar wind at the edge of the heliosphere) into two jet-like structures1-2. Magnetohydrodynamic simulations show that these heliospheric jets become unstable as they move down the heliotail1,3 and drive large-scale turbulence. However, the mechanism that produces of this turbulence had not been identified. Here we show that the driver of the turbulence is the Rayleigh-Taylor (RT) instability caused by the interaction of neutral H atoms streaming from the ISM with the ionized matter in the heliosheath (HS). The drag between the neutral and ionized matter acts as an effective gravity which causes a RT instability to develop along the axis of the HS magnetic field. A density gradient exists perpendicular to this axis due to the confinement of the solar wind by the solar magnetic field. The characteristic time scale of the instability depends on the neutral H density in the ISM and for typical values the growth rate is ~ 3 years. The instability destroys the coherence of the heliospheric jets and magnetic reconnection ensues, allowing ISM material to penetrate the heliospheric tail. Signatures of this instability should be observable in Energetic Neutral Atom (ENA) maps from future missions such as IMAP4. The turbulence driven by the instability is macroscopic and potentially has important implications for particle acceleration.

Progress on Understanding Rayleigh–Taylor Flow and Mixing Using Synergy Between Simulation, Modeling, and Experiment

Simultaneous advances in numerical methods and computing, theoretical techniques, and experimental diagnostics have all led independently to better understanding of Rayleigh–Taylor (RT) instability, turbulence, and mixing. In particular, experiments have provided significant motivation for many simulation and modeling studies, as well as validation data. Numerical simulations have also provided data that is not currently measurable or very difficult to measure accurately in RT unstable flows. Thus, simulations have also motivated new measurements in this class of buoyancy-driven flows. This overview discusses simulation and modeling studies synergistic with experiments and examples of how experiments have motivated simulations and models of RT instability, flow, and mixing. First, a brief summary of measured experimental and calculated simulation quantities, of experimental approaches, and of issues and challenges in the simulation and modeling of RT experiments is presented. Implicit large-eddy, direct numerical, and large-eddy simulations validated using RT experimental data are then discussed. This is followed by a discussion of modeling using analytical, modal, buoyancy–drag, and turbulent transport models of RT mixing experiments. The discussion will focus on three-dimensional RT mixing arising from multimode perturbations. Finally, this focused review concludes with a perspective on future simulation, modeling, and experimental directions for further research. Research in simulation and modeling of RT unstable flows, coupled with experiments, has made significant progress over the past several decades. This overview serves as an opportunity to both discuss progress and to stimulate future research on simulation and modeling of this unique class of hydrodynamically unstable turbulent flows.

Knudsen Number Effects on Two-Dimensional Rayleigh–Taylor Instability in Compressible Fluid: Based on a Discrete Boltzmann Method

Based on the framework of our previous work [H.L. Lai et al., Phys. Rev. E, 94, 023106 (2016)], we continue to study the effects of Knudsen number on two-dimensional Rayleigh–Taylor (RT) instability in compressible fluid via the discrete Boltzmann method. It is found that the Knudsen number effects strongly inhibit the RT instability but always enormously strengthen both the global hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) effects. Moreover, when Knudsen number increases, the Kelvin–Helmholtz instability induced by the development of the RT instability is difficult to sufficiently develop in the later stage. Different from the traditional computational fluid dynamics, the discrete Boltzmann method further presents a wealth of non-equilibrium information. Specifically, the two-dimensional TNE quantities demonstrate that, far from the disturbance interface, the value of TNE strength is basically zero; the TNE effects are mainly concentrated on both sides of the interface, which is closely related to the gradient of macroscopic quantities. The global TNE first decreases then increases with evolution. The relevant physical mechanisms are analyzed and discussed.

On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

In this article, we investigate the effect of surface tension in the Rayleigh–Taylor (RT) problem of stratified incompressible viscoelastic fluids. We prove that there exists an unstable solution to the linearized stratified RT problem with a largest growth rate Λ under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold $\vartheta _{c}$ ϑ c ). Moreover, for this instability condition, the largest growth rate $\varLambda _{\vartheta }$ Λ ϑ decreases from a positive constant to 0, when ϑ increases from 0 to $\vartheta _{c}$ ϑ c , which mathematically verifies that the internal surface tension can constrain the growth of the RT instability during the linear stage.

On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids

We study the nonlinear Rayleigh–Taylor (RT) instability of an inhomogeneous incompressible viscoelastic fluid in a bounded domain. It is well known that there exist strong solutions of RT instability in $H^{2}$ H 2 -norm in inhomogeneous incompressible viscoelastic fluids, when the elasticity coefficient κ is less than some threshold $\kappa _{\mathrm{C}}$ κ C . In this paper, we prove the existence of classical solutions of RT instability in $L^{1}$ L 1 -norm in Lagrangian coordinates based on a bootstrap instability method with finer analysis, if $\kappa <\kappa _{\mathrm{C}}$ κ < κ C . Moreover, we also get classical solutions of RT instability in $L^{1}$ L 1 -norm in Eulerian coordinates by further applying an inverse transformation of Lagrangian coordinates.

Evidence for Rayleigh-Taylor Plasma Instability at the Front of Solar Coronal Mass Ejections

This work focuses on the interaction of a Coronal Mass Ejection (CME) with the ambient solar corona, by studying the spatial and temporal evolution of the density fluctuations observed by the SOHO/UV Coronagraph Spectrometer (UVCS) during the CME. The investigation is performed by applying a wavelet analysis to the HI Ly α 1216 Å line intensity fluctuations observed with UVCS during the CME occurred on 24 December 2006. Strong and coherent fluctuations, with a significant spatial periodicity of about 84 Mm ≃ 0.12 R ⊙ , are shown to develop in about an hour along the front of the CME. The results seem to indicate the Rayleigh-Taylor (RT) instability, susceptible to the deceleration of the heavier fluid of the CME front into the lighter surrounding coronal plasma, as the likely mechanism underlying the generation of the observed plasma fluctuations. This could be the first inference of the RT instability in the outer solar corona in UV, due to the transit of a CME front in the quiet coronal plasma; this interpretation is also supported by a linear magnetohydrodynamic analysis of the RT instability.