Wavelength Perturbations Research Articles

Rayleigh–Plateau instability of anisotropic interfaces. Part 2. Limited instability of elastic interfaces

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Marangoni instability in a viscoelastic binary film with cross-diffusive effect

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Explosion of thin flat foils with periodical modified structure

The fast Z-pinch plasma formation, exploding dynamics, and the evolution of the instability can be controlled experimentally by making special structures on metal surface layer to change the initial state of material, which is valuable for studying the Z-pinch physics. Experiments on the explosion of thin flat foils which have been etched into a periodical structure on surface are performed on the QG-1 facility (～1.4 MA peak current, ～100 ns rise time) in order to study the effects of different surface conditions on explosion and control the evolution of the instability in fast Z-pinch plasma. A kind of inverse load configuration is used in experiment in which the return current post is set at the central axial-position and two modified flat foils are strained outside symmetrically as the main load. So the corresponding <i> <b>J</b> </i> × <i> <b>B</b> </i> force directs outward from the return current post orthogonal to the foil plane, creating an acceleration and pushing the foil plasma away from the center in this configuration. Different surfaces of the foil are also investigated in different conditions because of the asymmetric magnetic field distribution which is useful to study the different evolutions of instability. The foils used in the experiment mainly are the 30-μm-thick aluminum foil. The wavelength of groove perturbations seeded on the surface is 2 mm wide and ～10 μm deep. The plasma explosion dynamic behaviors around conditioned area are diagnosed by laser shadowgraphy, laser interferometry, multiframe optical self-emission imaging and B-dot. It is found that the initially etched periodical structure on surface can control the plasma structure in exploding process which can be concluded as follows. Developing plasma structure shows a periodic character similar to the initial surface structure and the eigenwavelength of the Al is suppressed. In the meantime, the surface without etched perturbations is also influenced by the etched side, showing a similar instability structure but with a lower amplitude. The correlation between two surfaces turns stronger than the case of normal foils. A faster expanding rate occurs in the deep region of the initial periodical groove structure which causes a reverse structure to form. In the discontinuous area of the conditoned structure, a narrow stream of plasma jets perpendicularly from the metal surface which causes a half-wavelength to occur in spectrum analysis. The magneto-hydro-dynamic theory analysis shows that the change of electrothermal instabilities is caused dominantly by the modulation of current density flowing around the periodical structure.

Instability of Dust–Acoustic Waves in Plasmas with Two-Temperature Nonthermal Ions

Theoretical and numerical investigations are carried out for the instability of the dust–acoustic waves (DAWs) under the transverse perturbation in a magnetized dusty plasma with two-temperature nonthermal ions. By the reductive perturbation technique, the Zakharov–Kuznetsov (ZK) equation and modified ZK equation of the DAWs are derived. Under the higher-order transverse perturbations, the instability growth rate of the soliton solutions of the ZK equations is studied. It is found that the most unstable wave mode exists in system. It is also noted that solitary waves are unstable when the ratio of the perturbation wave length to solitary wave width in the experimental coordinate is larger than a certain critical value.

Two- and three-dimensional simulations of Rayleigh–Taylor instabilities using a coupled Cahn–Hilliard/Navier–Stokes model

We report on two- and three-dimensional numerical simulations of Rayleigh–Taylor instabilities in immiscible fluids. A diffuse-interface model that combines the Cahn–Hilliard equation, governing the evolution of the volume fraction of one fluid, and the Navier–Stokes equations, governing the bulk velocity and pressure, is used. The study is limited to low Atwood numbers owing to the use of the Boussinesq approximation. The code is based on a pseudo-spectral method. A linear analysis is first performed in a two-dimensional case of Rayleigh–Taylor instability to confirm that the model very well captures this phenomenon in the case of inviscid or viscid fluids. One key aspect of this work is that the influence of the thermodynamic parameters related to the Cahn–Hilliard equation (interface thickness and mobility) is quantitively studied. Three-dimensional results of Rayleigh–Taylor instabilities in viscous fluids are then presented to show the possibilities of this modeling. We observe the effect of the viscosity and the wavelength of an initial single-mode perturbation on the mass transport during the nonlinear regime.

Waves on a compressed floating ice plate caused by motion of a dipole in water

Abstract

Instability of Thin Resistive Liners in the Linear Approximation

Magnetic implosion of liners is usually accompanied by the development of the Rayleigh–Taylor instability, which makes it hard to achieve high energy densities. However, the liners, which are thin compared with their skin layer (let us call them resistive), can also experience a different kind of instability, when parallel currents in different liner parts are attracted and draw these parts together dividing the liner into layers and filaments (filamentation or the tearing instability). We consider the problem of perturbation development in an infinitely thin resistive liner accounting for the distribution of the magnetic field, spread of currents, and flow of matter assuming that the perturbations are linear. Considering potential applications for different liner configurations (Z- and $\Theta $ -pinch liners and flat flyers) and the fact that the most destructive instabilities develop from the shortest wavelengths, we restrict our analysis to a planar case, which ignores the curvature of the liner and magnetic field lines. We find that the instability develops from any perturbation wavelengths, similar to the case of a perfectly conducting liner, with the instability growth rate for all the wavenumbers $k$ being of the order of $\sqrt {kg} $ ( $g$ is the liner acceleration), but always less than $\sqrt {kg} $ , and with the maximum growth rates for any directions of the wave vector k being greater than the growth rates of the perfectly conducting liner. One can often treat wire-array liners as resistive and, hence, use the results obtained for the description of instability development after the phase of merging the plasmas produced by individual wires.

Stability of hexagonal pattern in Rayleigh–Bénard convection for thermodependent shear-thinning fluids

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Self-consistent theory of the Darrieus–Landau and Rayleigh–Taylor instabilities with self-generated magnetic fields

The Rayleigh–Taylor (RT) and Darrieus–Landau (DL) instabilities are studied in an inertial confinement fusion context within the framework of small critical-to-shell density ratio DR and weak acceleration regime, i.e., large Froude number Fr. The quasi-isobaric analysis in Sanz et al. [Phys. Plasmas 13, 102702 (2006)] is completed with the inclusion of non-isobaric and self-generated magnetic-field effects. The analysis is restricted to perturbation wavelengths k−1 larger than the conduction length scale at the ablation front, yet its validity ranges from wavelengths shorter and larger than the conduction layer width (distance between the ablation front and the critical surface). The use of a sharp boundary model leads to a single analytical expression of the dispersion relation encompassing both instabilities. The two new effects come into play by modifying the perturbed mass and momentum fluxes at the ablation front. The momentum flux (perturbed pressure at the spike) is the predominant stabilizing mechanism in the RT instability (overpressure) and the driving mechanism in the DL instability (underpressure). The non-isobaric effects notably modify the scaling laws in the DL limit, leading to an underpressure scaling as ∼k−11/15 rather than ∼k−2/5 obtained in the quasi-isobaric model. The magnetic fields are generated due to misalignment between pressure and density gradients (Biermann battery effect). They affect the hydrodynamics by bending the heat flux lines. Within the framework of this paper, they enhance ablation, resulting in a stabilizing effect that peaks for perturbation wavelengths comparable to the conduction layer width. The combination of parameters DRFr2/3 defines the region of predominance of each instability in the dispersion relation. It is proven that the DL region falls outside of the parameter range in inertial confinement fusion.

Velocity and mass density of the ejecta produced from sinusoidal grooves in laser shock-loaded tin

When a shock wave of several tens of GPa breaks out at a free surface, a material is ejected ahead of this surface. The amount and velocity of such ejecta depend on the breakout pressure, state of the released material (solid, liquid, or mixed), whether the shockwave is supported or unsupported, and the initial geometrical perturbation (or roughness) of the free surface. If surface defects consist of small grooves, pits, or scratches, material ejection occurs in the form of jets breaking up into tiny particles (so-called microjetting), with jet tip velocities up to several times higher than the free surface velocity. The laser-based experiments presented in this paper focus on microjetting in shock-melted tin with periodic surface perturbations. Several complementary diagnostics are combined to measure the velocity and mass of ejecta during the early stages of the jetting process. One relevant advancement is the use of ps-laser x-ray radiography to probe the density of the ejecta in distinct jets a few tens of μm-wide. The effects of the depth and wavelength of the initial perturbation are investigated in both linear and near-linear growth regimes. The results are compared with predictions derived from the Richtmyer–Meshkov Instability theory.

Effective Interfacial Tension Effect on Kelvin-Helmholtz Instability

The instability of the plane interface between two uniform, superposed and streaming Walters′ B′ viscoelastic fluids through porous medium in the presence of effective interfacial tension is considered. The case of two uniform streaming fluids separated by a horizontal boundary is studied. It is observed, for the special case where the effective interfacial tension is ignored, that the system is stable or unstable for the potentially stable configuration which is in contrast to the case of Rivlin-Ericksen viscoelastic fluid or Newtonian fluid where the system is always stable for the potentially stable configuration. Moreover, if the perturbations in the direction of streaming are ignored, then the perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming, whereas for perturbations in all other directions there exists instability for a certain wave number range. ‘Effective interfacial tension’ is able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities.

Line-drag damping of Alfvén waves in radiatively driven winds of magnetic massive stars

ABSTRACT Line-driven stellar winds from massive (OB) stars are subject to a strong line-deshadowing instability. Recently, spectropolarimetric surveys have collected ample evidence that a subset of Galactic massive stars hosts strong surface magnetic fields. We investigate here the propagation and stability of magnetoradiative waves in such a magnetized, line-driven wind. Our analytic, linear stability analysis includes line-scattering from the stellar radiation, and accounts for both radial and non-radial perturbations. We establish a bridging law for arbitrary perturbation wavelength after which we analyse separately the long- and short-wavelength limits. While long-wavelength radiative and magnetic waves are found to be completely decoupled, a key result is that short-wavelength, radially propagating Alfvén waves couple to the scattered radiation field and are strongly damped due to the line-drag effect. This damping of magnetic waves in a scattering-line-driven flow could have important effects on regulating the non-linear wind dynamics, and so might also have strong influence on observational diagnostics of the wind structure and clumping of magnetic line-driven winds.

Nonlinear dynamics and chaos regularization of one-dimensional pulsating detonations with small sinusoidal density perturbations

In this work, we explore the effect of initial density variation in the combustible mixture on the nonlinear dynamics of one-dimensional gaseous detonation propagation. Studies of nonlinear dynamical behavior of one-dimensional pulsating detonation are frequently based upon the reactive Euler simulations with one-step Arrhenius chemistry. In regions of the control parameters space, i.e., activation energy Ea, the 1-D detonation dynamics are shown to exhibit chaotic behavior at values of 28.5 and 30.0. Using small sinusoidal initial density perturbations, this investigation shows the emergence of various nonlinear temporal patterns as a function of the perturbation wavelength. It demonstrates that the cooperative behavior between the intrinsic instability and imposed small perturbation can lead to regularization of chaotic oscillations in one-dimensional gaseous pulsating detonation. Hence, by means of a small perturbation, an otherwise chaotic motion is rendered more stable and predictable. This result thus has implications for how intrinsically unstable detonation dynamics can be controlled.

Linear dark matter density perturbations: A Wigner approach

In the Newtonian regime, the dynamics of scalar field dark matter is governed by the Schrödinger-Poisson model. In the usual treatment, the model is represented in a hydrodynamic form, by introducing macroscopic quantities such as the density and the average velocity. Here, we discuss an alternative kinetic representation of the same model, by relying on the Wigner function. This representation contains the hydrodynamic formulation as a special case but allows accounting for possible velocity dispersion while the hydrodynamic representation allows none. It has also the advantage of making more explicit the limit, yielding the Vlasov regime. We discuss in particular the effect of the broadening of the Wigner function, arising from the statistical properties of the wave function, and show that it gives rise to a Landau-like damping that tends to suppress the gravitational instability for larger wave-length perturbations.

The magnetised Richtmyer–Meshkov instability in two-fluid plasmas

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Instability and interface coupling of coaxial liquid jets in a driving stream

The behavior of jet breakup and interface coupling in a co-flow focusing (CFF) process is studied theoretically. A physical model of coaxial liquid jets moving in an infinite annular driving stream is established, and the dimensionless dispersion relation for temporally axisymmetric perturbations is solved numerically. The effects of process parameters such as flow velocities, liquid physical properties, and radius ratio between the inner and outer jets on the jet instability are analyzed. The evolutions of interface perturbations are observed in CFF experiments, and the perturbation wavelengths under different liquid flow rates are measured in comparison with theoretical predictions. Moreover, the coupling of interface instabilities in CFF is studied through changing the radius ratio between the inner and outer liquid jets. In particular, two simplified single jet models under the assumption of minimum inner and outer liquid flow rates are proposed to reveal the transition from weak coupling to strong coupling of jet interfaces. This work provides great insight into the physical mechanism of interface instability in CFF advantageous for producing monodisperse microdroplets with fine robustness and high throughput.

Magnetized directly-driven ICF capsules: increased instability growth from non-uniform laser drive

Simulations anticipate increased perturbation growth from non-uniform laser heating for magnetized direct-drive implosions. At the capsule pole, where the magnetic field is normal to the ablator surface, the field remains in the conduction zone and suppresses non-radial thermal conduction; in unmagnetized implosions this non-radial heat-flow is crucial in mitigating laser heating imbalances. Single-mode simulations show the magnetic field particularly amplifying short wavelength perturbations, whose behavior is dominated by thermal conduction. The most unstable wavelength can also become shorter. 3D multi-mode simulations of the capsule pole reinforce these findings, with increased perturbation growth anticipated across a wide range of scales. The results indicate that high-gain spherical direct-drive implosions require greater constraints on the laser heating uniformity when magnetized.

The effect of pressure on the hydrodynamic stability limit of premixed flames

The effect of pressure on the hydrodynamic stability limits of lean methane–air premixed flames is investigated with Direct Numerical Simulation based on multi-step chemistry and using a simplified one-step chemistry formulation. The dependency on pressure p of the cut-off length scale λc, that separates stable from unstable wavelengths of the initial perturbation, is computed for a number of different conditions. An increase of pressure causes a significant decrease of the cut-off length, as observed already in previous simulations and experiments. However, this decrease cannot be ascribed only to the decreased flame thickness due to elevated pressures, but the cut-off is reduced significantly even if normalized by either the thermal flame thickness ℓT or the diffusive flame thickness ℓD. For the conditions analyzed, the cut-off can be well approximated by the power-law λc∝p−0.8, while the thermal and diffusive flame thicknesses, in accordance with previous experiments, are proportional and scale as ℓT∝ℓD∝p−0.3. Therefore, the non-dimensional cut-off scales as λc/ℓT∝λc/ℓD∝p−0.5. This behavior is linked to the increase of the Zeldovich number with pressure, caused by higher inner layer temperatures at higher pressures, which is a result of increased importance of chain termination reactions. The same behavior is observed also in a one-step chemistry approach if the Zeldovich number, appearing explicitly in the one-step model equations, is varied with pressure according to the results from multi-step chemistry. The analysis is extended to the non-linear phase of the instability, when typical strong cusps are observed on the flame surface, simulating a two-dimensional slot burner for different pressures; it is confirmed that the same pressure effects are observed also in more complex settings and in the non-linear regime.

Kinetic Simulation of Unsteady Detonation with Thermodynamic Nonequilibrium Effects

Thanks to its mesoscopic kinetic nature, the discrete Boltzmann method has a capability of investigating unsteady detonation with essential hydrodynamic and thermodynamic nonequilibrium effects. In this work, an efficient and precise reactive discrete Boltzmann method is employed to investigate the impact of the amplitude and wave length of the initial perturbation, as well as of the chemical heat on the evolution of unsteady detonation with nonequilibrium effects. It is shown that the initial perturbation amplitude only affects the unsteady detonation in the early period, and the detonation becomes self-similar with minor phase differences later on. For small wave lengths, the pressure increases faster with a higher oscillation frequency in the early period, but decreases soon afterwards. With increasing chemical heat release, the pressure and its oscillations increase, and the nonequilibrium effects become more pronounced, but the oscillatory period decreases. When the wave length or chemical heat release is small enough, there is no transverse wave or cellular pattern, and the two-dimensional unsteady detonation reduces to the one-dimensional case.

Numerical Studies on Propagation Mechanisms of Gaseous Detonations in the Inhomogeneous Medium

Numerical simulation of propagation mechanisms of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The motivation is to investigate the effect of artificial perturbations on the evolution or amplification of cellular instability. The results show that, without artificial perturbations, a planar ZND detonation can evolve into a fully-developed cellular detonation after a distance because of the amplification of the cellular instability. With the artificial perturbations evolved in, at the early stage, the artificial perturbations control the transverse wave spacing by suppressing the amplification of the cellular instability. However, after a steady-state, the cellular instability starts to amplify itself again and eventually transits to a fully-developed cellular detonation. It is demonstrated that the presence of the artificial perturbations delays the formation of the cellular detonation, and the increase of instability factor can slow down this delay. It is also found that, if the wavelength of the artificial perturbations is close to the transverse wave spacing of the cellular detonation in the homogeneous medium, synchronization of these two factors occurs, and hence a cellular detonation with extremely regular cell pattern is immediately formed. The temperature discontinuity causes the front to be more turbulent with the presence of weak triple-wave structure locally besides the natural transverse waves. The artificial perturbations can increase the intrinsic instability, and hence changes the propagation mechanism of the detonation front. In contrast, large artificial perturbations could prohibit the propagation but reduce cellular instability. It is concluded that the competition of artificial perturbations with intrinsic detonation instability dominates the evolution of cellular structures of the detonation front.