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The linear and nonlinear instability of a thin liquid film flowing down above or below (Rayleigh-Taylor instability) an inclined thick wall with finite thermal conductivity are investigated in the presence of slip at the wall-liquid interface. A nonlinear evolution equation for the free surface deformation is obtained under the lubrication approximation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated. When the film flows below the wall it will be subjected to destabilizing and stabilizing Marangoni numbers. It is found that from the point of view of the linear growth rate the flow destabilizes with slip in a wavenumber range. However slip stabilizes for larger wavenumbers up to the critical (cutoff) wavenumber. From the point of view of the maximum growth rate flow slip may stabilize or destabilize increasing the slip parameter depending on the magnitude of the Marangoni and Galilei numbers. Explicit formulas were derived for the intersections (the wavenumber for the growth rate and the Marangoni number for the maximum growth rate) where slip changes its stabilizing and destabilizing properties. From the numerical solution of the nonlinear evolution equation of the free surface profiles, it is found that slip may suppress or stimulate the appearance of subharmonics depending on the magnitudes of the selected parameters. In the same way, it is found that slip may increase or decrease the nonlinear amplitude of the free surface deformation. The effect of the thickness and finite thermal conductivity of the wall is also investigated. [ABSTRACT FROM AUTHOR]

The linear and nonlinear thermocapillary instability of a liquid layer located above or below a thick horizontal wall with slip effect under gravity is investigated for the first time. A nonlinear evolution equation for the free surface deformation is obtained under the lubrication approximation. The curves of linear growth rate, maximum growth rate and critical Marangoni number are calculated under two physical conditions. First, gravity is directed from the liquid to the wall and has a stabilizing effect. Second, gravity is directed from the wall to the liquid (Rayleigh-Taylor instability). In the latter case, the liquid film is also subjected to stabilizing and destabilizing Marangoni numbers. The film is subjected to slip at the thick wall with finite thermal conductivity. A very important result is that slip is not always destabilizing. From the point of view of the growth rate, the slip parameter β changes its destabilizing role into a stabilizing one at a particular wavenumber, independent of β . Also, from the standpoint of the maximum growth rate, the slip parameter β is not always destabilizing. Magnitudes of the Marangoni number were found where β is stabilizing. Formulas to delimit where the role of β changes are derived analytically. The free surface profiles obtained from the nonlinear evolution equation show the stabilizing and destabilizing effects of the parameters. It is revealed that the Rayleigh-Taylor instability can be delayed, before the film free surface touches the wall. [ABSTRACT FROM AUTHOR]

Abstract The flow of an active thermal protection system exploiting subsonic counter-flow jets for wing leading edges of hypersonic vehicles is numerically studied on the basis of the three dimensional Navier-Stokes equations. The coolant air issuing from around the stagnation point as an array of three jets spreads over both the upper and the lower sides of the cylinder surface and about 40 ~ 60% cooling effectiveness is achieved in the range up to 5 degrees angle of attack despite the occurrence of various three-dimensional fluid-dynamic instabilities. The numerical scheme is second order accurate but simple inclusion of high order polynomial approximation in the reconstruction enables the capturing of finer structure of the flow field.

The present outbreak enables the researchers from fluid mechanics to widen the understanding of expelling respiratory liquids from a unique perspective to diminish the persistence of COVID-19. This article focuses on uncovering the instability mechanism responsible for forming droplets and aerosols during respiratory events such as breathing, talking, coughing and sneezing. We illustrate a mathematical framework by revisiting the model (Vadivukkarasan and Panchagnula, 2017) and show the associated instabilities during respiratory events. We envisage the combined Rayleigh–Taylor–Kelvin–Helmholtz (R–T–K–H) model as a robust tool for respiratory events. This study highlights the distinct possibility of respiratory droplet formation over multiple instabilities and provides a fundamental understanding. We present the different dominant modes through a ternary phase diagram for three-dimensional numbers (Bond number and Weber numbers). Furthermore, this model can be extended phenomenologically to viscous fluids to satisfy mucus and saliva in the respiratory liquids. [ABSTRACT FROM AUTHOR]

The stability characteristics of an inviscid, incompressible and immiscible cylindrical interface are examined using linear temporal theory. The cylindrical interface is subjected to two instability mechanisms, namely Rayleigh–Taylor (R–T) and Kelvin–Helmholtz (K–H) instabilities. The combined action of R–T and K–H in the presence of surface tension is investigated for a hollow jet in an unbounded liquid medium and reported. The problem includes the motion in an axial direction (K–H mechanism) and the radial direction (R–T mechanism) to destabilize the interface. The instability behavior is described by a few operating parameters, namely, Bond number (Bo), Weber number (We) and Atwood number (A). Here, Bond number is attributed to R–T instability whereas Weber number is attributed to K–H instability. The temporal analysis reveals that the Bond number plays a significant role in determining the dominant growth rate, most unstable axial wavenumber and cut-off axial wavenumber. Furthermore, it is also shown through dimensionless energy budget arguments, even a small amount of energy in the radial motion causes the most unstable wavenumber associated with primary atomization to increase significantly. [ABSTRACT FROM AUTHOR]

The Richtmyer-Meshkov and the Rayleigh-Taylor instabilities of viscoplastic (or the Bingham) fluids are studied in the three-dimensional formulation of the problem. A numerical modeling of the intermixing of two fluids with different rheology, whose densities differ twice, as a result of instabilities development process has been carried out. The development of the Richtmyer-Meshkov and the Rayleigh-Taylor instabilities of the Bingham fluids is analyzed utilizing the MacCormack and the Volume of Fluid (VOF) methods to reconstruct the interface during the process. Both the results of numerical simulation of the named instabilities of the Bingham liquids and their comparison with theory and the results of the Newtonian fluid simulation are presented. Critical amplitude of the initial perturbation of the contact boundary velocity field at which the development of instabilities begins was estimated. This critical amplitude presents because of the yield stress exists in the Bingham fluids. Results of numerical calculations show that the yield stress of viscoplastic fluids essentially affects the nature of the development of both Rayleigh-Taylor and Richtmyer-Meshkov instabilities. If the amplitude of the initial perturbation is less than the critical value, then the perturbation decays relatively quickly, and no instability develops.When the initial perturbation exceeds the critical amplitude, the nature of the instability development resembles that of the Newtonian fluid. In a case of the Richtmyer-Meshkov instability, the critical amplitudes of the initial perturbation of the contact boundary at different values of the yield stress are estimated. There is a distinction in behavior of the non-Newtonian fluid in a plane case: with the same value of the yield stress in three-dimensional geometry, the range of the amplitude values of the initial perturbation, when fluid starts to transit from rest to motion, is significantly narrower. In addition, it is shown that the critical amplitude of the initial perturbation of the contact boundary for the Rayleigh-Taylor instability is lower than for the Richtmyer-Meshkov instability. This is due to the action of gravity, which helps the instability to develop and counteracts the forces of viscous friction.

The potential of water hammer events for igniting hydrogen-oxygen mixtures was examined in an experimental study. Compression waves simulating water-hammer events were created by projectile impact on a piston in a water-filled pipe terminated by a test section filled with gas. Triangular wave forms with peak pressures up to 50 MPa propagated through the piping system and compressed the gas in the test section. Experiments were carried out with both air and hydrogen-oxygen gas mixtures using high-speed video of the transparent test section, dynamic pressure and spectroscopic measurements to examine the motion of the water-gas interface and determine ignition thresholds. The impulsive acceleration of the water-gas interface and deceleration created by the compression of the gas resulted in Richtmyer-Meshkov and Rayleigh-Taylor instabilities that grew to create large distortions of the initially planar and horizontal water-gas interface. The gas layer was compressed in volume by up to a factor of 50 and the gas pressures increased to as high as 20 MPa within 2 to 4 ms. The distortion of the water surface during compression resulted in a significant increase in interfacial area and ultimately, creation of a two-phase mixture of water and compressed gas. Some ignition events were observed, but the dispersion and mixing of water with the gas almost completely suppressed the pressure rise during the ignition transient. Only by eliminating the instability of the water interface with a solid disk between the water and gas were we able to observe consistent ignition with significant pressure rises associated with the combustion. [ABSTRACT FROM AUTHOR]

The flow of an active thermal protection system exploiting subsonic counter-flow jets for wing leading edges of hypersonic vehicles is numerically studied on the basis of the three dimensional Navier-Stokes equations. The coolant air issuing from around the stagnation point as an array of three jets spreads over both the upper and the lower sides of the cylinder surface and about 40 ~ 60% cooling effectiveness is achieved in the range up to 5 degrees angle of attack despite the occurrence of various three-dimensional fluid-dynamic instabilities. The numerical scheme is second order accurate but simple inclusion of high order polynomial approximation in the reconstruction enables the capturing of finer structure of the flow field. [ABSTRACT FROM AUTHOR]

By modifying a physical property of a solution like its density or viscosity, chemical reactions can modify and even trigger convective flows. These flows in turn affect the spatiotemporal distribution of the chemical species. A nontrivial coupling between reactions and flows then occurs. We present simple model systems of this chemo-hydrodynamic coupling. In particular, we illustrate the possibility of chemical reactions controlling or triggering viscous fingering, Rayleigh–Taylor, double-diffusive, and convective dissolution instabilities. We discuss laboratory experiments performed to study these phenomena and compare the experimental results to theoretical predictions. In each case we contrast the chemo-hydrodynamic patterns and instabilities with those that develop in nonreactive systems and unify the different dynamics in terms of the common features of the related spatial mobility profiles. [ABSTRACT FROM AUTHOR]

Density variations in fluid flows can arise due to acoustic or thermal fluctuations, compositional changes during mixing of fluids with different molar masses, or phase inhomogeneities. In particular, thermal and compositional (with miscible fluids) density variations have many similarities, such as in how the flow interacts with a shock wave. Two limiting cases have been of particular interest: (a) the single-fluid non-Oberbeck–Boussinesq low–Mach number approximation for flows with temperature variations, which describes vertical convection, and (b) the incompressible limit of mixing between miscible fluids with different molar masses, which describes the Rayleigh–Taylor instability. The equations describing these cases are remarkably similar, with some differences in the molecular transport terms. In all cases, strong inertial effects lead to significant asymmetries of mixing, turbulence, and the shape of mixing layers. In addition, density variations require special attention in turbulence models to avoid viscous contamination of the large scales. [ABSTRACT FROM AUTHOR]

Removal of mantle lithosphere by Rayleigh‐Taylor (R‐T) instabilities is invoked to explain the formation of high plateaus and mountain ranges. Here we report geochemical and microstructural observations from mantle xenoliths from Lunar Crater volcanic field, central Nevada, which we interpret to directly sample a R‐T instability beneath the Basin and Range. The xenoliths comprise a suite of mylonitic and granular peridotites with fertile and refractory major and trace element compositions, suggesting a mantle lithospheric origin. Temperatures calculated using several geothermometers are 1,200–1,300 °C, in contrast to xenoliths from other localities in the Basin and Range (typically ~1,000 °C). High Lunar Crater temperatures suggest the xenoliths originate from the base of the mantle lithosphere. The mylonitic peridotites exhibit olivine deformation microstructures characteristic of deformation in the dislocation creep regime; orthopyroxenes experienced brittle deformation. Recrystallized grain sizes (~80 μm) suggest the mylonites deformed at ~50 MPa. Recrystallized olivines demonstrate isochemical deformation, suggesting the ~50‐MPa differential stresses were achieved at ~1,200 °C, implying strain rates of 2 × 10−9 to 4 × 10−7/s, and corresponding to effective viscosities of 8.9 × 1013 to 1.4 × 1016 Pa/s. The most plausible mechanism for producing such conditions in the deep lithosphere beneath central Nevada is extreme strain localization within an actively deforming R‐T instability. The most highly strained samples have relatively low effective viscosities, suggesting that strain is preferentially partitioned into weaker rocks within the deforming lithosphere. This study highlights the importance of strain localization and associated weakening as mechanisms for facilitating lithospheric R‐T instabilities. Key Points: Granular and mylonitic peridotites from Lunar Crater volcanic field (central Nevada) originate from the base of the mantle lithosphereMylonites deformed at ~1200°C and may directly sample an active Rayleigh‐Taylor instability beneath the Basin and RangeStrain localization in narrow shear zones accommodates lithospheric R‐T instabilities [ABSTRACT FROM AUTHOR]

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det ⁡ ∇ ψ (x , t) = G ∘ ψ (x , t). The novelty of our approach is a new so-called perturbation formulation of MA, which constructs the solution map ψ via composition of a sequence of near-identity deformations of a reference mesh. Then, we formulate a new version of the deformation method [21] that results in a simple, fast, and high-order accurate numerical scheme and a dynamic SAM algorithm that is of optimal complexity when applied to time-dependent mesh generation for solutions to hyperbolic systems such as the Euler equations of gas dynamics. We perform a series of challenging 2 D and 3 D mesh generation experiments for grids with large deformations, and demonstrate that SAM is able to produce smooth meshes comparable to state-of-the-art solvers [22,18] , while running approximately 200 times faster. The SAM algorithm is then coupled to a simple Arbitrary Lagrangian Eulerian (ALE) scheme for 2 D gas dynamics. Specifically, we implement the C -method [64,65] and develop a new ALE interface tracking algorithm for contact discontinuities. We perform numerical experiments for both the Noh implosion problem as well as a classical Rayleigh-Taylor instability problem. Results confirm that low-resolution simulations using our SAM-ALE algorithm compare favorably with high-resolution uniform mesh runs. • We develop a new fast algorithm for smooth adaptive meshing (SAM) for gas dynamics. • Uses a novel formulation in terms of near-identity perturbations of a uniform mesh. • A high order accurate and fast deformation method is implemented. • SAM is up to two orders of magnitude faster than other state-of-the-art schemes. • Applications to 2D ALE gas dynamics simulations show speed-up over uniform runs. [ABSTRACT FROM AUTHOR]

In this work, the temporal–spatial evolution of kinetic and thermal energy dissipation rates in three-dimensional (3D) turbulent Rayleigh–Taylor (RT) mixing are investigated numerically by the lattice Boltzmann method. The temperature fields, kinetic and thermal energy dissipation rates with temporal–spatial evolution, the probability density functions, the fractal dimension of mixing interface, spatial scaling law of structure function for the kinetic and the thermal energy dissipation rates in 3D space are analysed in detail to provide an improved physical understanding of the temporal–spatial dissipation-rate characteristic in the 3D turbulent Rayleigh–Taylor mixing zone. Our numerical results indicate that the kinetic and thermal energy dissipation rates are concentrated in areas with large gradients of velocity and temperature with temporal evolution, respectively, which is consistent with the theoretical assumption. However, small scale thermal plumes initially at the section of half vertical height increasingly develop large scale plumes with time evolution. The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times t/τ ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. It is further demonstrated that the second, fourth and sixth-order structure functions for velocity and temperature structure functions have a linear scaling within the inertial range.

Atomization of liquid fuel jets by cross-flowing airstream is critical to the performance of many aerospace combustors. Recent advances in numerical methods and increases in computational power have enabled the first principle, high fidelity simulation of this phenomenon. In the recent past we presented a detailed validation and analysis of such simulations against experimental data at ambient conditions. At combustor operating conditions, however, both temperature and pressure are significantly elevated. In this work we extend the same computational approach to the study of the impact of reduced liquid–gas density ratio due to increased air density associated with operating pressure elevation on the atomization physics. The previously validated ambient condition case is used as the baseline for comparison with three cases with decreasing density ratios. The density ratio is independently varied by adjusting the gas density and velocity together so that the momentum flux ratio and Weber number are maintained constant. The global-scale jet penetration and trajectory are slightly modified as the density ratio varies. The most significant changes are observed for the local processes of liquid breakup and atomization. As the density ratio is independently reduced, a transition of dominance from the Rayleigh–Taylor to the Kelvin–Helmholtz instability mechanisms on the liquid column surface is detected by analyzing the vorticity fields. Such a transition is verified using linear stability analyses and is also shown to be consistent with the simulation results of a non-monotonic variation of surface wavelength with density ratio. Downstream, a counter-rotating vortex pair (CVP) arises as the density ratio is reduced, the physical origins of which are similar to those documented for gaseous jet in cross-flow studies. Atomization effectiveness is reduced downstream with reduced density ratio and this is in agreement with experimental observation. This result is explained in terms of the density-ratio-related velocity-ratio changes that allow for a switch in behavior from a faster to a slower crossflow speed with respect to the liquid. As a result, at low density ratio recoiling of stretched structures and possibility of increased collision result in increasing Sauter Mean Diameter (SMD). [ABSTRACT FROM AUTHOR]

Abstract: In the current paradigm, magma primarily exists in the crust as a crystalline mush containing distributed melt lenses. If a melt‐rich (or fluid) lens is less dense than the overlying mush, then Rayleigh‐Taylor (RT) instabilities will develop and could evolve into spheroids of ascending melt. Due to contrasting melt‐mush rheologies, the theoretical RT instability wavelength can be orders of magnitude larger than the magmatic system. We explored how this confinement affects the gravitational stability of melt lenses through laboratory experiments with pairs of liquids with one layer much thinner and up to 2.2·105 times less viscous than the other; we extended the viscosity ratio to 106 with linear stability analysis. We found the growth rate of a bounded RT instability is approximately ΔρgD 6 π μ 2, where Δρ is the difference in density between the fluids, g is gravity, D is the container diameter, and μ2 is the viscosity of the thicker viscous layer. This differs from the unbounded case, where the growth rate also depends on the thickness and viscosity of the thin, low‐viscosity layer. Applying the results to melt lenses in magmatic mushes, we find that for the ranges of expected rheologies, the timescales for development of the instability, and the volumes of packets of rising melt generated span very wide ranges. They are comparable with the frequencies and sizes of volcanic eruptions and episodes of unrest and so suggest that RT instabilities in mush systems can cause episodic volcanism. [ABSTRACT FROM AUTHOR]

The effect of competing Rayleigh-Taylor and Kelvin-Helmholtz mechanisms of instability applied to a cylindrical two-fluid interface is discussed. A three-dimensional temporal linear stability model for the instability growth is developed based on the frozen time approximation. The fluids are assumed to be inviscid and incompressible. From the governing equations and the boundary conditions, a dispersion relation is derived and analyzed for instability. Four different regimes have been shown to be possible, based on the most unstable axial and circumferential wavenumbers. The four modes are the Taylor mode, the sinuous mode, the flute mode and long and short wavelength helical modes. The effect of Bond number, Weber number, and density ratio are investigated in the context of the mode chosen. It is found that Bond number is the primary determinant of the neutral stability while Weber number plays a key role in identifying the instability mode that is manifest. A regime map is presented to delineate the modes realized for a given set of flow parameter values. From this regime map, a short wavelength helical mode is identified which is shown to result only when both the Rayleigh-Taylor and Kelvin-Helmholtz instability mechanisms are active. A scaling law for the magnitude of the wavenumber vector as a function of Bond number andWeber number are also developed. A length scale is defined to characterize the interface distortion. Using this length scale, the set of conditions where the interface exhibits a maximum in surface area creation is identified. With the objective of achieving the smallest characteristic length scale of interface distortion, a criterion to optimally budget mean flow energy is also proposed. [ABSTRACT FROM AUTHOR]

Entropy generation rates in two-dimensional Rayleigh–Taylor (RT) turbulence mixing are investigated by numerical calculation. We mainly focus on the behavior of thermal entropy generation and viscous entropy generation of global quantities with time evolution in Rayleigh–Taylor turbulence mixing. Our results mainly indicate that, with time evolution, the intense viscous entropy generation rate s u and the intense thermal entropy generation rate S θ occur in the large gradient of velocity and interfaces between hot and cold fluids in the RT mixing process. Furthermore, it is also noted that the mixed changing gradient of two quantities from the center of the region to both sides decrease as time evolves, and that the viscous entropy generation rate 〈 S u 〉 V and thermal entropy generation rate 〈 S θ 〉 V constantly increase with time evolution; the thermal entropy generation rate 〈 S θ 〉 V with time evolution always dominates in the entropy generation of the RT mixing region. It is further found that a “smooth” function 〈 S u 〉 V ∼ t 1 / 2 and a linear function 〈 S θ 〉 V ∼ t are achieved in the spatial averaging entropy generation of RT mixing process, respectively.

We present a novel technique for solving for the flow of a viscous multi-fluid system in which interfaces are present. The Navier-Stokes equations are used in their exact form, without the need for phase-field approximations. A Boussinesq-type approach is invoked, in which the component fluids of differing densities are represented by a single fluid in which the density changes smoothly but rapidly across each narrow interfacial zone. This formulation is illustrated in detail for classical planar Rayleigh-Taylor flow containing two horizontal layers of fluid, in which the upper fluid has greater density. The interface between the fluids is therefore unstable and overturns as time progresses. The results of this new approach are compared against the predictions of classical Boussinesq theory and a recent Extended Boussinesq model proposed by the authors. Finally, a comparison with the predictions of a smoothed-particle-hydrodynamics model gives strong support for this new technique. • Novel model for interfacial flows of viscous fluids. • New solution algorithms. • Accurate solutions for Rayleigh-Taylor problem. • Verified results using SPH code. [ABSTRACT FROM AUTHOR]

In this paper we investigate the effect of surface tension on hydromagnetic Rayleigh-Taylor (R-T) instability of two incompressible superimposed fluids in a porous medium with suspended dust particles immersed in a uniform horizontal magnetic field. The relevant linearized perturbation equations have been solved using normal mode technique and the dispersion relation is derived analytically for the considered system. The dispersion relation is influenced by the simultaneous presence of medium porosity, suspended dust particles, permeability, magnetic field and surface tension. The onset criteria of R-T stability and instability are obtained and discussed. The growth rate of R-T instability is calculated numerically and it is affected by the simultaneous presence of surface tension and magnetic field. The effects of various parameters on the growth rate of the R-T instability are discussed. [ABSTRACT FROM AUTHOR]

A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. The importance of using DNS to calibrate and assess RANS type turbulence models is also highlighted. [ABSTRACT FROM AUTHOR]

The Navier-Stokes characteristic boundary conditions (NSCBC) approach is extended to compressible Rayleigh-Taylor flow (CRT-F) with variable acceleration histories, whose time- and space- dependent open boundaries challenge the available methods. The non-reflecting boundary conditions are realized by combining CRTF's physical boundary conditions and NSCBC's idea, and by appending a dissipation region, where physics-consistent viscous terms are introduced to realize non-reflection without additional effect. Numerical tests confirm the effectiveness and robustness of newly proposed schemes. [ABSTRACT FROM AUTHOR]

This paper presents a new, improved version of the K–L model, as well as a detailed investigation of K–L and multi-fluid models with reference to high-resolution implicit large eddy simulations of compressible Rayleigh–Taylor mixing. The accuracy of the models is examined for different interface pressures and specific heat ratios for Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1 . It is shown that the original version of the K–L model requires modifications in order to provide comparable results to the multi-fluid model. The modifications concern the addition of an enthalpy diffusion term to the energy equation; the formulation of the turbulent kinetic energy (source) term in the K equation; and the calculation of the local Atwood number. The proposed modifications significantly improve the results of the K–L model, which are found in good agreement with the multi-fluid model and implicit large eddy simulations with respect to the self-similar mixing width; peak turbulent kinetic energy growth rate, as well as volume fraction and turbulent kinetic energy profiles. However, a key advantage of the two-fluid model is that it can represent the degree of molecular mixing in a direct way, by transferring mass between the two phases. The limitations of the single-fluid K–L model as well as the merits of more advanced Reynolds-averaged Navier–Stokes models are also discussed throughout the paper. [ABSTRACT FROM AUTHOR]

We study the effect of self-generated magnetic fields in two-dimensional computer models of blast-wave driven high-energy density Rayleigh-Taylor instability (RTI) experiments. Previous works [1,2] suggested that such fields have the potential to influence the RTI morphology and mixing. When neglecting the friction force between electrons and ions, we do indeed find that dynamically important ( β ≲ 10 3 ) magnetic fields are generated. However, in the more realistic case where the friction force is accounted for, the resulting fields are much weaker, β ≳ 10 5 , and can no longer influence the dynamics of the system. Although we find no evidence for dynamically important magnetic fields being created in the two-dimensional case studied here, the situation might be different in a three-dimensional setup, which will be addressed in a future study. [ABSTRACT FROM AUTHOR]

Investigation of buoyancy driven mixing by volumetric energy deposition is of particular interest to inertial confinement fusion research. This contribution describes a new microwave facility and an experiment to study buoyancy driven mixing of miscible fluids by volumetric energy deposition. A light weakly-polar fluid initially rested on top of a heavier and higher polarity fluid. As the fluid system was subjected to microwave radiation, less microwave energy was deposited into the weakly-polar fluid than the higher polarity fluid; thus, the bottom fluid was preferentially heated, and its density decreased due to thermal expansion. With continued microwave heating, the density of the bottom fluid dropped below the density of the upper fluid, creating a Rayleigh–Taylor unstable configuration, and, subsequently, buoyancy driven mixing. The miscible pair of toluene and tetrahydrofuran was chosen for the volumetric energy deposition experiments presented. Initially, single fluid microwave heating experiments, for which the source term in the heat equation was varied by variations in the fluid volume, were performed to provide calibration of a mathematical model. The model provided a prediction of the neutral stability point of the system, which facilitated experimental design and understanding. Measurements of the mixing layer width from this two-fluid mixing experiment are compared with results from a self-similar analysis of the governing equations. [ABSTRACT FROM AUTHOR]

We investigate the possibility of stabilizing a Rayleigh–Taylor experiment by imposing a small upward temperature gradient. We find that if the two fluids have equal thermal conductivities nothing can be accomplished. If either thermal conductivity is much greater than the other, the small gradient is always stabilizing. If the thermal conductivities are of the same order of magnitude the small gradient can be stabilizing or destabilizing depending on the thermal expansion coefficients. We have used a Darcy model so that we can derive formulas and present a physical explanation of what we find. [ABSTRACT FROM AUTHOR]

Jackson et al. ( this volume ) used 3D seismic reflection data to describe intrasalt deformation in salt walls in the Santos Basin. They focused on the origin of enigmatic allochthonous salt sheets of older evaporites (A1 unit) emplaced above overlying stratified evaporites (A2–A4 units). Their kinematic model incorporates: (i) initial inward flow and thickening of A1 salt within the rising wall, and arching of A2–A4 overburden; (ii) breaching of the arched overburden, ascent of mobile A1 evaporites along single or multiple feeders, and emplacement of upper-wall sheets or canopies; and (iii) a component of regional shortening within the salt. This companion paper uses physical modelling to explain how and why these structures occur and proposes a mechanical basis for the kinematic model. Our first two models simulated salt having uniform internal density, with walls growing by (i) initially symmetric differential loading and (ii) initially symmetric differential loading plus shortening. These models reproduced anticlines and injection folds seen in the simpler deformed walls in the Santos Basin. However, neither model reproduced the most complex structures within the Santos evaporites, which are: (i) allochthonous intrusions, (ii) steep feeders, and (iii) recumbent synclines. Thus, differential loading and shortening alone are insufficient to generate these complex structures. In our third model, a less-dense lower evaporite (A1) was overlain by denser upper evaporites (A2–A4), similar to the density structure found by Santos Basin wellbores. The wall rose solely by differential loading. In this model, A1 breached the overlying evaporites to form vertical diapirs feeding salt sheets and salt wings in the upper part of the salt wall. Breakthrough of A1 folded A2–A4 evaporites into recumbent synclines. Model sections closely resemble Santos seismic examples, suggesting that the key to forming these complex intrasalt structures is a density inversion within the evaporite sequence that creates a Rayleigh–Taylor instability. [ABSTRACT FROM AUTHOR]

We discuss a model for the evolution of the turbulent mixing width $$h(t)$$ after a shock or a reshock passes through the interface between two fluids of densities $$\rho _A$$ and $$\rho _B$$ inducing a velocity jump $$\Delta V$$ . In this model, the initial growth rate is independent of the surface finish or initial mixing width $$h_0$$ , but its duration $$t^{*}$$ is directly proportional to it: $$h(t)=h_0 +2\alpha A\Delta Vt$$ for $$0\le t\le t^{*}$$ , and $$h(t)=h^{*}({1+(\dot{h}^{*}/\theta h^{*})(t-t^{*})})^{\theta }$$ for $$t\ge t^{*}$$ . Here $$A$$ is the Atwood number $$(\rho _B -\rho _A)/(\rho _B +\rho _A), \alpha $$ and $$\theta $$ are dimensionless, $$A$$ -dependent parameters measured in past Rayleigh-Taylor experiments, and $$\beta $$ is a new dimensionless parameter we introduce via $$t^{*}=(h_0 /\Delta V)\beta $$ . The mixing width $$h$$ and its derivative $$\dot{h}$$ remain continuous at $$t=t^{*}$$ since $$h^{*}=h_0 +2\alpha A\Delta Vt^{*}$$ and $$\dot{h}^{*}=2\alpha A\Delta V$$ . We evaluate $$\beta \sim 6$$ at $$A\approx 0.7$$ from air/SF $$_{6}$$ experiments and propose that the transition at $$t=t^{*}$$ signals isotropication of turbulence. We apply this model to the recent experiments of Jacobs et al. (Shock Waves 23:407-413, ) on shock and reshock, and discuss briefly the third wave causing an unstable acceleration of the interface. We also consider the experiments of Weber et al. (Phys Fluids 24:074105, ) and argue that their smaller growth rates reflect density gradient stabilization. [ABSTRACT FROM AUTHOR]

Findings from an experimental investigation of the break-up of liquid curtains are reported, with the overall aim of examining stability windows for multi-layer liquid curtains composed of Newtonian fluids, where the properties of each layer can be kept constant or varied. For a single-layer curtain it is known that the minimum flow rate required for initial stability can be violated by carefully reducing the flow rate below this point, which defines a hysteresis region. However, when two or three layers are used to form a composite curtain, the hysteresis window can be considerably reduced depending on the experimental procedure used. Extensive quantitative measurements of this hysteresis region are provided alongside an examination of the influence of physical properties such as viscosity and surface tension. The origins of curtain break-up for two different geometries are analysed; first where the curtain width remains constant, pinned by straight edge guides; and second where the curtain is tapered by angled edge guides. For both cases, the rupture speed is measured, which appears to be consistent with the Taylor-Culick velocity. Observations of the typical linearly spaced jets which form after the break-up has transpired and the periodicity of these jets are compared to the Rayleigh-Taylor wavelength and previous experimental measurements. Furthermore, the curtain stability criterion originally developed by Brown (1961), summarised in terms of a Weber number, has recently been extended to multi-layer curtains by Dyson et al. (2009); thus this report provides the first experimental measurements which puts this to the test. Ultimately, it is found that only the most viscous and polymer-based liquids violate this criterion. [ABSTRACT FROM AUTHOR]

Direct numerical simulation of mixing processes (Rayleigh-Taylor and Richtmyer-Meshkov instabilities) is computationally expensive due to the need to resolve turbulent structures on small scales. Hence, it is common practice in both academia and industry to use phenomenological models that explicitly model the mixing processes within a host hydrodynamic code. For such schemes to be self-consistent, the mixing should be dominated by the mass introduced by the dedicated mixing model, with minimal contribution from the numerical methods of the host code. In this report, several diagnostic statistics are described that allow for the assessment of the production of mix and a determination of the quality of a mixing model. These diagnostics are implemented within an existing two-dimensional finite element hydrocode, containing an implementation of Youngs' turbulent mix model, and used to assess the mixing scheme against a number of two-fluid test problems. [ABSTRACT FROM AUTHOR]

We present a feasability study for a laser-driven shock experiment on the National Ignition Facility (NIF) to study the evolution of the Rayleigh-Taylor instability in the non-linear regime. The experiment is relevant to the problem of material mixing in core-collapse supernovae and is intended to serve as a stepping stone for more realistic Rayleigh-Taylor experiments using spherical geometry. The radiation hydrodynamics simulations described here are done using the CRASH code and include the actual NIF laser drive. It is shown that the simulations are converged with respect to numerical resolution effects. Small-scale imperfections, such as they might be introduced during the process of target fabrication, are found to have negligible impact, provided that their size is smaller than 1 μm. The simulation results are in excellent agreement with a buoyancy-drag model, and the mix layer width is found to increase at higher drive energies. [ABSTRACT FROM AUTHOR]

Abstract: A preliminary design of an experiment meant to investigate the evolution of multimode Rayleigh–Taylor instability (RT) is presented. This experiment is intended to provide a direct measurement of the two-dimensional bubble front evolution in the hydrodynamic regime. RT growth for the proposed design has been analyzed using one-dimensional direct numerical simulations in Hyades and models of self-similar behavior. The models predictions are compared to results obtained in two-dimensional Dafna numerical simulations, with good agreement. The proposed design assures a significant bubble-merging process (∼3–4 bubble merger generations). The design takes advantage of the National Ignition Facility (NIF) capabilities to provide a large enough laser spot area (∼0.5–1 cm2), along with a low-enough drive that preheat effects remain small. [Copyright &y& Elsevier]

The stability of several density profiles constructed from a linear combination of step functions in a vertically orientated two-dimensional porous medium are considered. A quasi-steady-state approximation is made so that the initial stability of the system can be approximated. Using a similar approach to that of Tan and Homsy (Phys Fluids 29:3549-3556, ) a dispersion equation for each density profile is obtained analytically at time zero. Neutral stability curves are then obtained to allow the regions of the parameter space to be divided into stable and unstable regions. [ABSTRACT FROM AUTHOR]

We study the problem of reactive Rayleigh–Taylor turbulence in the Boussinesq framework using one-dimensional-turbulence (ODT) simulations. In this problem a reaction zone between overlying heavy/cold reactants and underlying light/hot products moves against gravity. First, we show that ODT results for global quantities in non-reactive Rayleigh–Taylor turbulence are within those from direct numerical simulations (DNS). This comparison give us confidence in using ODT to study unexplored flow regimes in the reactive case. Then, we show how ODT predicts an early stage of reactive Rayleigh–Taylor turbulence that behaves similarly to the non-reactive case, as observed in previous DNS. More importantly, ODT indicates a later stage where the growth of the reaction zone reduces considerably. The present work can be seen as a step towards the study of supernova flames with ODT. [ABSTRACT FROM AUTHOR]

An experiment that seeks to investigate buoyancy driven mixing of miscible fluids by microwave volumetric energy deposition is presented. The experiment involves the use of a light, non-polar fluid that initially rests on top of a heavier fluid which is more polar. Microwaves preferentially heat the polar fluid, and its density decreases due to thermal expansion. As the microwave heating continues, the density of the lower fluid eventually becomes less than that of the upper, and buoyancy driven Rayleigh-Taylor mixing ensues. The choice of fluids is crucial to the success of the experiment, and a description is given of numerous fluid combinations considered and characterized. After careful consideration, the miscible pair of toluene / tetrahydrofuran (THF) was determined as having the best potential for successful volumetric energy deposition buoyancy driven mixing. Various single fluid calibration experiments were performed to facilitate the development of a heating theory. Thereafter, results from two-fluid mixing experiments are presented that demonstrate the capability of this novel Rayleigh-Taylor driven experiment. Particular interest is paid to the onset of buoyancy driven mixing and unusual aspects of the experiment in the context of typical Rayleigh-Taylor driven mixing. [ABSTRACT FROM AUTHOR]

Abstract: Buoyancy-driven convection can be induced by concentration and temperature gradients near the interface between two immiscible fluids filling a vertical Hele–Shaw cell, each of them containing a reactant of an exothermic reaction taking place in the bulk of the lower layer. A chemo-hydrodynamical pattern appears then due to the combined action of Rayleigh–Taylor, diffusive layer convection and Rayleigh–Bénard instabilities occurring either below or above the interface. The mathematical model we develop to describe such dynamics consists in a set of reaction–diffusion–advection equations ruling the evolution of concentrations and temperature coupled to Navier–Stokes equation, written in a Hele–Shaw approximation. We perform numerical simulations of the non-linear system and study the influence on pattern formation of changes in the Damköhler number of the problem and in the ratio of initial reactant concentrations. [Copyright &y& Elsevier]

Abstract: The nonlinear evolution of two fluid interfacial structures such as bubbles and spikes arising due to the combined action of Rayleigh–Taylor and Kelvin–Helmholtz instability is investigated. Using Layzer''s model analytic expressions for the asymptotic value of the combined growth rate are obtained in both cases for spikes and bubbles. However, if the overlying fluid is of lower density the interface perturbation behaves in different ways. Depending on the magnitude of the velocity shear associated with Kelvin–Helmholtz instability both the bubble and spike amplitude may simultaneously grow monotonically (instability) or oscillate with time. [Copyright &y& Elsevier]

Abstract: Fluid instabilities like Rayleigh–Taylor (R–T), Richtmyer–Meshkov (R–M) and Kelvin–Helmholtz (K–H) instability can occur in a wide range of physical phenomenon from astrophysical context to Inertial Confinement Fusion (ICF). Using Layzer''s potential flow model, we derive the analytical expressions of growth rate of bubble and spike for ideal magnetized fluid in R–T and R–M cases. In the presence of transverse magnetic field, the R–M and R–T instabilities are suppressed or enhanced depending on the direction of magnetic pressure and hydrodynamic pressure. Again the interface of two fluid may oscillate if both the fluids are conducting. However, it is observed that the magnetic field has no effect in linear case. [Copyright &y& Elsevier]