Rayleigh-Taylor Instability Research Articles

Nonlinear Rayleigh–Taylor instability in an accelerated soap film

Rupture and fragmentation of thin liquid films are of great importance in manufacturing, agriculture, disease transmission, and other fields. An individual rupture event typically results from the nonlinear growth of small perturbations excited by the classical Rayleigh–Taylor mechanism and opposed by surface tension on the film interfaces. We study an initially uniform liquid film accelerated in the direction perpendicular to its interfaces, constructing a new reduced description of the flow in the limit of large surface tension consisting of three coupled (nonlinear) partial differential equations. This system is linearly unstable to disturbances of small wavenumber; we derive a simplified asymptotic description to gain analytical understanding of the nonlinear development until rupture. An initial phase of exponential film thinning leads to the accumulation of liquid in a central bulge. At a well-defined time, a localised pinch-off mechanism, driven by a mismatch in the interfacial curvature at the edge of the bulge, results in a self-similar thinning that breaks the film in finite time. Across a wide parameter range, the resultant droplet formed from the central bulge contains a significant fraction of the initial film volume.

Quasi-irrotational approximation for the Rayleigh-Taylor instability in a solid bounded by a rigid wall

Quasi-irrotational approximation for the Rayleigh-Taylor instability in a solid bounded by a rigid wall

The effect of relative position on the motion and interactions of particle sedimentation under gravity in a finite-width vertical channel

Understanding the settling behaviour of particles and the interactions between fluid and particles in channelled fluids is crucial for various natural and industrial processes. The research presented in this study focuses on elucidating the sedimentation modes of dual particles within finite-width channels, employing the Arbitrary Lagrangian-Eulerian (ALE) method in conjunction with Hertz contact theory. We aim to understand how the initial relative position affects the dynamic characteristics of particle settlement. The threshold values of α = 35° and gap ratio (the distance between particles relative to their diameter) L/D = 3.5 are deemed critical. The phenomenon of particles ‘kissing’ does not manifest when the initial angle α ≤ 35°. As the α increases, the DKT (Drafting-Kissing-Tumbling) process recurs at earlier stage. In all cases where dual-particle are arranged in a vertically aligned pattern (D P1 = D P2 or DP1> DP2 ), the settling behaviour of particles will eventually achieve a steady state characterized by the DKT process when L/D ≤ 4.0. As the gap ratio (L/D) increases, the time taken for the kissing phenomenon is prolonged. Additionally, the two particles exchange positions and the larger particle taking the lead in the settling process. In scenarios where dual particles are arranged side by side, the kissing phenomenon does not occur. Instead, the trajectory of the particles deviates from the centreline and shifts towards the channel wall due to the Magnus effect when L/D ≤ 2.0. When L/D ≥ 3.0, particles settle as though they were a single particle. In cases involving multiple particles, the hindering effect of the wall becomes significant and can not be ignored, leading to the observation of Rayleigh-Taylor instability development. As a result, the overall settlement pattern tends to be ‘concave’.

Rayleigh-Taylor instability in inhomogeneous relativistic classical and degenerate electron-ion magnetoplasmas

Abstract We study the Rayleigh-Taylor instability (RTI) of electrostatic plane wave perturbations in compressible relativistic magnetoplasma fluids with thermal ions under gravity in three different cases of when (i) electrons are in isothermal equilibrium, i.e., classical or nondegenerate, (ii) electrons are fully degenerate (with $T_e=0$), and (iii) electrons are partially degenerate or have finite temperature degeneracy (with $T_e\neq0$). While in the cases of (i) and (iii), we focus on the regimes where the particle's thermal energy is more or less than the rest mass energy, i.e., $\beta_e \equiv k_{\mathrm B}T_e/{m_ec^2}<1~\rm{or}~>1$, the case (ii) considers from weakly to ultra-relativistic degenerate regimes. A general expression of the growth rate of instability is obtained and analyzed in the three different cases relevant to laboratory and astrophysical plasmas, which generalize and advance the previous theory on RTI.

Groundwater-Driven Evolution of Prebiotic Alkaline Lake Environments.

Alkaline lakes are thought to have facilitated prebiotic synthesis reactions on the early Earth because their modern analogs accumulate vital chemical feedstocks such as phosphate through the evaporation of dilute groundwaters. Yet, the conditions required for some building block synthesis reactions are distinct from others, and these conditions are generally incompatible with those permissible for nascent cellular function. However, because current scenarios for prebiotic synthesis have not taken account of the physical processes that drive the chemical evolution of alkaline lakes, the potential for the co-occurrence of both prebiotic synthesis and the origins and early evolution of life in prebiotic alkaline lake environments remains poorly constrained. Here, we investigate the dynamics of active, prebiotically relevant alkaline lakes using near-surface geophysics, aqueous geochemistry, and hydrogeologic modeling. Due to their small size, representative range of chemistry, and contrasting evaporation behavior, the investigated, neighboring Last Chance and Goodenough Lakes in British Columbia, Canada offer a uniquely tractable environment for investigating the dynamics of alkaline lake behavior. The results show that the required, extreme phosphate enrichments in alkaline lake waters demand geomorphologically-driven vulnerability to evaporation, while the resultant contrast between evaporated brines and inflowing groundwaters yields Rayleigh-Taylor instabilities and vigorous surface-subsurface cycling and mixing of lake and groundwaters. These results provide a quantitative basis to reconcile conflicting prebiotic requirements of UV light, salinity, metal concentration, and pH in alkaline lake environments. The complex physical and chemical processing inherent to prebiotic alkaline lake environments thus may have not only facilitated prebiotic reaction networks, but also provided habitable environments for the earliest evolution of life.

Scale Invariant Bounds for Mixing in the Rayleigh–Taylor Instability

Scale Invariant Bounds for Mixing in the Rayleigh–Taylor Instability

Numerical investigation of instabilities in over-pressured magnetized relativistic jets

Relativistic jets from active galactic nuclei are observed to be collimated on the parsec scale. When the pressure between the jet and the ambient medium is mismatched, recollimation shocks and rarefaction shocks are formed. Previous numerical simulations have shown that instabilities can destroy the recollimation structure of jets. In this study, we aim to study the instabilities of nonequilibrium over-pressured relativistic jets with helical magnetic fields. Especially, we investigate how the magnetic pitch affects the development of instabilities. We performed 3D relativistic magnetohydrodynamic simulations for different magnetic pitches, as well as a 2D simulation and a relativistic hydrodynamic simulation which served as comparison groups In our simulations, Rayleigh-Taylor instability (RTI) is triggered at the interface between the jet and ambient medium in the recollimation structure of the jet. We find that when the magnetic pitch decreases, the growth of RTI becomes weak but, interestingly, another instability -- the current-driven (CD) kink instability -- is excited. The excitement of CD kink instability after passing the recollimation shocks can match the explanation of the quasi-periodic oscillations observed in BL Lac qualitatively.

Self-generated magnetic field in three-dimensional ablative Rayleigh–Taylor instability

The self-generated magnetic field in three-dimensional (3-D) single-mode ablative Rayleigh–Taylor instability (ARTI) relevant to the acceleration phase of a direct-drive inertial confinement fusion (ICF) implosion is investigated. It is found that stronger magnetic fields up to a few thousand teslas can be generated by 3-D ARTI rather than by its two-dimensional (2-D) counterpart. The Nernst effects significantly alter the magnetic field convection and amplify the magnetic fields. The magnetic field of thousands of teslas yields the Hall parameter of the order of unity, leading to profound magnetized heat flux modification. While the magnetic field significantly accelerates the bubble growth in the short-wavelength 2-D modes through modifying the heat fluxes, the magnetic field mostly accelerates the spike growth but has little influence on the bubble growth in 3-D ARTI. The accelerated growth of spikes in 3-D ARTI is expected to enhance material mixing and degrade ICF implosion performance. This work is focused on a regime relevant to direct-drive ICF parameters at the National Ignition Facility, and it also covers a range of key parameters that are relevant to other ICF designs and hydrodynamic/astrophysical scenarios.

Simulation study of the impacts of E-region density on the growth of equatorial plasma bubbles

Equatorial plasma bubbles (EPBs) in the ionospheric F region are notorious for causing severe scintillation in radio signals, posing significant challenges for communication and navigation systems. Understanding and forecasting EPB occurrence is crucial from a space weather perspective, given their impact on satellite and terrestrial communication. In this study, we present the impacts of E-region conductivity on the generation of EPBs by using the 3D high-resolution bubble (HIRB) model. By changing the production rate of NO+ ions in the E region, the flux-tube-integrated linear growth rate of the Rayleigh–Taylor instability can be modified. Multiple simulation runs show that even a moderate variation of the growth rate turns into a significant difference in EPB growth into the top of the ionosphere. This is a major factor that has made forecasting EPB generation quite difficult for several decades.

Rayleigh-Taylor instability in multiple finite-thickness fluid layers

Rayleigh-Taylor instability in multiple finite-thickness fluid layers

Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective

The Rayleigh–Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and areal density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.

Insights into fractal space features in nonlinear electrohydrodynamic Rayleigh–Taylor instability of viscous fluids

This paper describes a unique method for detecting and evaluating nonlinear Rayleigh–Taylor instability (RTI) in electro-viscous fluids exposed to an external vertical electric field. The governing equations are based on a linearized Navier–Stokes framework with nonlinear boundary conditions, capturing the system's complexity. Using a traveling wave transformation, the analysis reduces the system's complicated dynamics to a nonlinear characteristic equation in the elevation function that includes quadratic and cubic nonlinearities. The strategy utilizes El-Dib's frequency formula, which allows for the derivation of an equivalent linearized form of the characteristic equation, simplifying the nonlinear equation and making it more tractable for analytical investigation. The study emphasizes the critical function of the electric field in the system's stability. Smaller electric fields improve stability and equilibrium, resulting in damped oscillations that maintain the fluid–fluid interface. Larger electric fields, on the other hand, enhance instabilities, causing the system to behave nonlinearly, which might lead to chaotic motion if the oscillations are severe. The analysis is extended to convert the characteristic equation into a fractal space description. The fractal derivative form enables the modeling and study of complicated, nonlinear, and chaotic processes commonly encountered in fluid dynamics problems. This methodology is especially well-suited to handling multi-scale dynamics and nonlinear growth in RTI. The influence of fractal factors on system behavior is examined. Increasing the fractal order consistently has a stabilizing effect, lowering the oscillation amplitude and increasing damping, hence improving stability. In contrast, raising the fractalness parameter introduces a destabilizing influence, resulting in bigger oscillations and lower damping, destabilizing the system over time. This study sheds light on the behavior of nonlinear RTI in electro-viscous fluids in the presence of electric fields and fractal dynamics.

An adaptive level-set/square-root-conformation representation/discontinuous Galerkin method for simulating viscoelastic two-phase flow systems

A new numerical method, which is based on the coupling of adaptive mesh technique, level set (LS) method, square-root-conformation representation (SRCR) approach, and discontinuous Galerkin (DG) method within the dual splitting framework, is developed for viscoelastic two-phase flow problems. This combination has been more effective than expected. The LS method is performed to capture the moving interface due to its efficiency and simplicity when dealing with the significant interface deformations. The dual splitting scheme is applied to decouple the whole system into subequations, which circumvent the limitation of the Ladyzhenskaya-Babuška-Brezzi condition. The SRCR approach is employed to reconstruct the Oldroyd-B constitutive equation to solve the high Weissenberg number problem. The high-order DG method is performed for the spatial discretizations of equations to deal with the convection-dominated problems. In addition, the reinitialization method of the LS function and a simple mass correction technique are applied to guarantee the mass conservation in calculation. In this coupled method, there is no need to require reinitialization within every time step but after suitable time steps. Meanwhile, the adaptive mesh technique is implemented in the coupling procedure, which greatly improves the computational efficiency. The coupled algorithm is performed to simulate the swirling deformation flow, Rayleigh–Taylor instability and bubble rising problems. And the influences of the parameters on the rising speed and shape of bubble in viscoelastic liquid are analyzed in detail. The numerical results indicate that the coupled algorithm is effective and accurate for simulating the interface evolution problems with complex topological structure changes, and can guarantee the mass conservation property.

Onset of kinetic effects on Rayleigh–Taylor instability: Advective–diffusive asymmetry

Onset of kinetic effects on Rayleigh–Taylor instability: Advective–diffusive asymmetry

Onset of cabbeling instabilities in superconfined two-fluid systems

Convective-driven mixing in permeable subsurface environments is relevant in engineering and natural systems. This process occurs in groundwater remediation, oil recovery, CO2 sequestration, and hydrothermal environments. When two fluids come into contact in superconfined geometries like open fractures in rocks, complex molecular dynamics can develop at the fluid–fluid interface, creating a denser mixture and leading to cabbeling instabilities that propel solutal convection. Previous studies in superconfined systems have used models based on unstable density distributions—generating Rayleigh–Taylor instabilities—and analog fluid mixtures characterized by nonlinear equations of state—resulting in cabbeling dynamics—yet often neglecting interfacial tension effects, which is also relevant in miscible systems. This study incorporates the Korteweg tensor into the Hele–Shaw model to better understand the combined influence of geometry confinement and interfacial tension on the onset of cabbeling instabilities in two-fluid superconfined systems. Through direct numerical simulations, we investigate the system's stability, revealing that the onset, characterized by the critical time tc, exhibits a nonlinear relationship with the system's nondimensional parameters—the Rayleigh number Ra, the anisotropy ratio ϵ, and the Korteweg number Ko. This relationship is crystallized into a single scaling law tc=F(Ra,ϵ,Ko). Our findings indicate that geometry and effective interfacial tension exert a stabilizing effect during the initial stages of convection, stressing the necessity for further exploration of its influence on fluid mixing in superconfined systems.

Dimming events of evolved stars due to clouds of molecular gas

Context. The dramatic dimming episode of the red supergiant Betelgeuse in 2019 and 2020, caused by a partial darkening of the stellar disk, has highlighted gaps in the understanding of the evolution of massive stars. Aims. We analyzed numerical models to investigate the processes behind the formation of dark surface patches and the associated reduction in the disk-integrated stellar light. Methods. With the CO5BOLD code, we performed global 3D radiation-hydrodynamical simulations of evolved stars, including convection in the stellar interior, self-excited pulsations, and the resulting atmospheric dynamics with strong radiative shocks. Results. We attribute dimming phenomena to obscuring clouds of cool gas in the lower atmosphere, forming according to three different scenarios. One process transports material outward in a strong shock, similar to what occurs in 1D simulations of radially pulsating asymptotic giant branch (AGB) stars. However, in 3D models, deviations from spherical symmetry of the shock front can lead to further local density enhancements. Another mechanism is triggered by a large convective upflow structure, in combination with exceptionally strong radial pulsations. This induces Rayleigh-Taylor instabilities, causing plumes of material to be sent outward into the atmosphere. The third and rarest scenario involves large-amplitude convective fluctuations, leading to enhanced flows in deep downdrafts, which rebound and send material outward. In all cases, the dense gas above the stellar surface cools and darkens rapidly in visible light. AGB stars show localized dark patches regularly during intermediate phases of their large-amplitude pulsations, while more massive stars will only intermittently form such patches during luminosity minima. Conclusions. The episodic levitation of dense gas clumps above the stellar surface, followed by the formation of complex molecules in the cooling gas and possibly dust grains at a later stage, can account for the dark patches and strong dimming events of supergiant stars such as Betelgeuse.

Understanding the nonlinear behavior of Rayleigh–Taylor instability with a vertical electric field for perfect dielectric fluids

It is well known that, influenced only by gravity, the fluid interface is unstable when a light fluid supports a heavy fluid and is stable when a heavy fluid supports a light fluid. The situation becomes much more complicated when a vertical electric field is externally applied to the dielectric fluids. We present a nonlinear perturbation solution for an unstable interface between two incompressible, inviscid, immiscible, and perfectly dielectric fluids in the presence of vertical electric fields and gravity in two dimensions. Our nonlinear stability analysis shows that even when the linear theory indicates that the interface is stable, this system is actually unstable. The destabilization effects of the vertical electric field always dominate when gravity provides stabilization effects. This is true even when the applied vertical electric field is very weak. Analytical expressions for the overall amplitude and velocity of the interface are derived up to an arbitrary order in terms of the initial perturbation amplitude and are displayed explicitly up to the fourth order. A comparison study between the predictions of the nonlinear perturbation solution and the numerical results shows that the derived solutions capture the primary nonlinear behavior of the unstable fluid interface. By analyzing the electrical force at the interface, we provide theoretical explanations for the nonlinear phenomena induced by the vertical electric field.

Large-field high-resolution X-ray AKB microscope for measuring hydrodynamic instabilities at the SG-III prototype laser facility

X-ray imaging with a large field of view (FOV) and high resolution is extremely important for Rayleigh–Taylor instability measurement with a small amplitude and high spatial frequency in laser inertial confinement fusion. We developed an advanced Kirkpatrick–Baez (AKB) microscope based on the quadratic-aberration theory to realize a large FOV and high resolution. This microscope was assembled and tested in a laboratory, and it was then successfully applied for imaging the hydrodynamic instability of a perturbation target in implosion experiments at the Shenguang-III prototype laser facility. Imaging results demonstrate that the AKB microscope can achieve an optimal resolution of ~ 0.53 μm and ~ 0.40 μm and a spatial resolution of < 1.5 μm within a 300-µm FOV and < 4.5 μm in a 1-mm FOV.

DISCRETE-PULSE INPUT OF ENERGY AS INCREASE IN THE EFFICIENCY OF SUGAR PRODUCTION

The article describes techniques and technologies of domestic sugar production, technologies for obtaining and subsequent purification of diffusion juice. The use of discrete-pulse energy input is proposed to increase the efficiency and improve the purification of the diffusion juice. The efficiency of sugar beet raw material processing largely depends on its quality, production technology and subsequent purification of the diffusion juice. The current state of equipment and technology of domestic sugar production does not ensure the sufficient completeness of sucrose extraction from beets, highly effective lime-carbonic acid purification, as a result of which it does not ensure the achievement of world average indicators. The solution to these problems is the improvement of the existing and the creation of innovative technologies for sugar beet processing using the method of discrete-pulse energy input (DPEI). The technological results of the verification of the method of saturation in the RPA confirmed that with the same energy consumption, expressed by the turbulent dissipated energy, the pulsating effects are more effective than the stationary process. At the same time, part of the energy goes to the formation of the dispersion surface and, mainly, its recovery, which compensates for coalescence, and the other part goes to the deformation of this surface under the action of turbulent pulsations. The application of the DPEI and RPA method for its implementation in the sugar industry allows the processes of mixing, dispersion, dissolution, heating, and homogenization to be carried out simultaneously in one apparatus. Rotor-pulsation devices can replace cavitation devices, homogenizers, dispersers, because when passing through their working organs (stator-rotor), the liquid is exposed not only to cavitation, but also to the action of shock waves, interphase turbulence, penetrating cumulative microcurrents, eddies, which causes interphase Rayleigh-Taylor or Kelvin-Helmholtz instability surfaces, which leads to intense crushing of dispersed inclusions, an increase in the total contact surface of the phases, and an increase in heat and mass transfer processes. Similar effects are unattainable when using traditional cavitation devices.

Energy-consistent discretization of viscous dissipation with application to natural convection flow

A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and by requiring that continuous identities like the product rule are mimicked discretely. The proposed viscous dissipation function has a quadratic, strictly dissipative form, for both simplified (constant viscosity) stress tensors and general stress tensors. The proposed expression is not only useful in evaluating energy budgets in turbulent flows, but also in natural convection flows, where it appears in the internal energy equation and is responsible for viscous heating. The viscous dissipation function is such that a consistent total energy balance is obtained: the ‘implied’ presence as sink in the kinetic energy equation is exactly balanced by explicitly adding it as source term in the internal energy equation.Numerical experiments of Rayleigh–Bénard convection (RBC) and Rayleigh–Taylor instabilities confirm that with the proposed dissipation function, the energy exchange between kinetic and internal energy is exactly preserved. The experiments show furthermore that viscous dissipation does not affect the critical Rayleigh number at which instabilities form, but it does significantly impact the development of instabilities once they occur. Consequently, the value of the Nusselt number on the cold plate becomes larger than on the hot plate, with the difference increasing with increasing Gebhart number. Finally, 3D simulations of turbulent RBC show that energy balances are exactly satisfied even for very coarse grids. Therefore, the proposed discretization also forms an excellent starting point for testing sub-grid scale models and is a useful tool to assess energy budgets in any turbulence simulation, with or without the presence of natural convection.