Wavelength Perturbations Research Articles

Freeze-out of perturbation growth of single-mode helium–air interface through reflected shock in Richtmyer–Meshkov flows

‘Freeze-out’ of amplitude growth, i.e. the amplitude growth stagnation of a shocked helium–air interface, is realized through a reflected shock, which produces baroclinic vorticity of the opposite sign to that deposited by the first shock. Theoretically, a model is constructed to calculate the relations among the initial parameters for achieving freeze-out. In particular, if the amplitude growth is within the linear regime at the arrival of the reflected shock, the time interval between the impacts of two shock waves is linearly related to the initial perturbation wavelength, and is independent of the initial perturbation amplitude. Experimentally, an air–SF $_6$ (or air–argon) plane interface is adopted to produce a weak reflected shock. Seven experimental runs with specific initial conditions are examined. For all cases, freeze-out is achieved after the reflected shock impact under the designed conditions.

Nonlinear ablative Rayleigh-Taylor instability: Increased growth due to self-generated magnetic fields.

The growth rate of the nonlinear ablative Rayleigh-Taylor (RT) instability is enhanced by magnetic fields self-generated by the Biermann battery mechanism; a scaling for this effect with perturbation height and wavelength is proposed and validated with extended-magnetohydrodynamic simulations. The magnetic flux generation rate around a single RT spike is found to scale with the spike height. The Hall parameter, which quantifies electron magnetization, is found to be strongly enhanced for short-wavelength spikes due to Nernst compression of the magnetic field at the spike tip. The impact of the magnetic field on spike growth is through both the suppressed thermal conduction into the unstable spike and the Righi-Leduc heat flow deflecting heat from the spike tip to the base. Righi-Leduc is found to be the dominant effect for small Hall parameters, while suppressed thermal conduction dominates for large Hall parameters. These results demonstrate the importance of considering magnetic fields in all perturbed inertial confinement fusion hot spots.

A Positive Feedback Between Crustal Thickness and Melt Extraction for the Origin of the Martian Dichotomy.

A North/South difference in crustal thickness is likely at the origin of the Martian dichotomy in topography. Recent crustal thickness maps were obtained by inversion of topography and gravity data seismically anchored at the InSight station. On average, the Martian crust is 51-71km thick with a southern crust thicker by 18-28km than the northern one. The origin of this crustal dichotomy is still debated although the hypothesis of a large impact is at present very popular. Here, we propose a new mechanism for the formation of this dichotomy that involves a positive feedback between crustal growth and mantle melting. As the crust is enriched in heat-producing elements, the lid of a one-plate planet is hotter and thinner where the crust is thicker, inducing a larger amount of partial melt below the lid and hence a larger rate of melt extraction and crustal growth. We first demonstrate analytically that larger wavelength perturbations, that is, hemispherical perturbations, grow faster because smaller wavelengths are more attenuated by thermal diffusion. We then use a parameterized thermal evolution model with a well-mixed mantle topped by two different lids characterized by their thermal structures and thicknesses to study the growth of the crust in the two hemispheres. Our results demonstrate that this positive feedback can generate a significant crustal dichotomy.

On the Stability of Surface Growth: The Effect of a Compliant Surrounding Medium

AbstractIn a recent paper Abeyaratne et al. (J. Mech. Phys. Solids 167:104958, 2022) concerning the stability of surface growth of a pre-stressed elastic half-space with surface tension, it was shown that steady growth is never stable, at least not for all wave numbers of the perturbations, when the growing surface is traction-free. On the other hand, steady growth was found to be always stable when growth occurred on a flat frictionless rigid support and the stretch parallel to the growing surface was compressive. The present study is motivated by these somewhat unexpected and contrasting results.In this paper the stability of a pre-compressed neo-Hookean elastic half-space undergoing surface growth under plane strain conditions is studied. The medium outside the growing body resists growth by applying a pressure on the growing surface. At each increment of growth, the incremental change in pressure is assumed to be proportional to the incremental change in normal displacement of the growing surface. It is shown that surface tension stabilizes a homogeneous growth process against small wavelength perturbations while the compliance of the surrounding medium stabilizes it against large wavelength perturbations. Specifically, there is a critical value of stretch,$\lambda _{\mathrm{cr}} \in (0,1)$λcr∈(0,1), such that growth is linearly stable against infinitesimal perturbations ofarbitrarywavelength provided the stretch parallel to the growing surface exceeds$\lambda _{\mathrm{cr}}$λcr. Thisstability threshold,$\lambda _{\mathrm{cr}}$λcr, is a function of the non-dimensional parameter$\sigma \kappa /G^{2}$σκ/G2, which is the ratio between two length-scales$\sigma /G$σ/Gand$G/\kappa $G/κ, where$G$Gis the shear modulus of the elastic body,$\sigma $σis the surface tension, and$\kappa $κis the stiffness of the surrounding compliant medium.It is shown that$(a)$(a)$\lambda _{\mathrm{cr}} \to 1$λcr→1as$\kappa \to 0$κ→0and$(b)$(b)$\lambda _{\mathrm{cr}} \to 0^{+}$λcr→0+as$\kappa \to \infty $κ→∞, thus recovering the results in Abeyaratne et al. (J. Mech. Phys. Solids 167:104958, 2022) pertaining to the respective limiting cases where growth occurs$(a)$(a)on a traction-free surface and$(b)$(b)on a frictionless rigid support. The results are also generalized to include extensional stretches.

Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction–diffusion equations

We consider a class of singularly perturbed 2-component reaction–diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow–fast–slow, interfaces between stable homogeneous rest states. In many example systems, such as models of desertification fronts in dryland ecosystems, such fronts can exhibit an instability by which the interface destabilizes into fingering patterns. Motivated by the appearance of such patterns, we propose two versions of a 2D stability criterion for (transversal) long wavelength perturbations along the interface of these traveling slow–fast–slow fronts. The fronts are constructed using geometric singular perturbation techniques by connecting slow orbits on two distinct normally hyperbolic slow manifolds through a heteroclinic orbit in the fast problem. The associated stability criteria are expressed in terms of the nonlinearities of the system and the slow–fast–slow structure of the fronts. We illustrate and further elaborate on the general set-up by explicitly working out the existence and transversal (in)stability of traveling fronts in a number of example systems/models. We analytically establish the instability of invading bare soil/vegetation interfaces against transversal long wavelength perturbations in several dryland ecosystem models and numerically recover fingering vegetation patterns counter-invading an invading desertification front.

Superharmonic instability for regularized long-wave models* *JCB is supported by NSF DMS-1615418. VMH is supported by NSF DMS-2009981.

We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include the regularized Boussinesq, Benney–Luke, and Benjamin–Bona–Mahony equations. Of particular interest is a striking new instability phenomenon—spectrum off the imaginary axis extending into infinity. The spectrum of the linearized operator of the generalized Korteweg–de Vries equation, for instance, lies along the imaginary axis outside a bounded set. The spectrum for a regularized long-wave model, by contrast, can vary markedly with the parameters of the periodic traveling waves. We perform rigorous spectral asymptotics for short wavelength perturbations to establish conditions under which the spectrum tends to infinity along the imaginary axis or some curve whose real part is nonzero. We conduct numerical experiments which corroborate our analytical findings.

Green function for linearized Navier–Stokes around a boundary shear layer profile for long wavelengths

This paper is the continuation of a program, initiated in Grenier and Nguyen [SIAM J. Math. Anal. 51 (2019); J. Differential Equations 269 (2020)], to derive pointwise estimates on the Green function of Orr–Sommerfeld equations. In this paper we focus on long wavelength perturbations, more precisely horizontal wave numbers \alpha of order \nu^{1/4} , which correspond to the lower boundary of the instability area for monotonic profiles.

Fragmentation of faceted crystalline wires

The reduction of surface energy is a well-known driving force for the fragmentation of nanowires. Fragmentation can limit the service life of those small low-dimensional building blocks or can be controlled to induce beneficial shape changes. For isotropic surface energy, fragmentation is analogous to the classic Rayleigh-Plateau instability of liquid jets. However, commonly synthesized crystalline nanowires have strongly anisotropic surface energies and exhibit facets coinciding with cusps in the Wulff plot. Depending on growth orientation, different fragmentation behaviors have been seen in nanowires. Using phase-field simulations, we show that fragmentation of faceted nanowires with cubic crystal symmetry may occur by a finite-amplitude nonlinear instability, as opposed to a Rayleigh-Plateau-like linear instability, depending on nanowire growth orientation. We carry out a weakly nonlinear analysis based on sharp interface theory to characterize the faceted nanowire shape corresponding to a surface-energy saddle point. The analysis predicts that the minimum amplitude of a periodic shape perturbation to trigger fragmentation increases with cusp strength but decreases inversely proportionally to the perturbation wavelength for long wavelengths, in good quantitative agreement with phase-field predictions. The results provide the theoretical foundation to predict nanowire stability as a function of length and surface energy in diverse applications.

On the Short Wave Instability of the Liquid/Gas Contact Surface in Porous Media

We consider a problem of hydrodynamic stability of the liquid displacement by gas in a porous medium in the case when a light gas is located above the liquid. The onset of instability and the evolution of the small shortwave perturbations are investigated. We show that when using the Darcy filtration law, the onset of instability may take place at an infinitely large wavenumber when the normal modes method is inapplicable. The results of numerical simulation of the nonlinear problem indicate that the anomalous growth of the amplitude of shortwave small perturbations persists, but the growth rate of amplitude decreases significantly compared to the results of linear analysis. An analysis of the stability of the gas/liquid interface is also carried out using a network model of a porous medium. It is shown that the results of surface evolution calculations obtained using the network model are in qualitative agreement with the results of the continual approach, but the continual model predicts a higher velocity of the interfacial surfaces in the capillaries. The growth rate of perturbations in the network model also increases with decreasing perturbation wavelength at a constant amplitude.

Investigating the Role of Gravity Waves on Equatorial Ionospheric Irregularities Using TIMED/SABER and C/NOFS Satellite Observations

In this paper, for the first time, simultaneous atmospheric temperature perturbation profiles obtained from the TIMED/SABER satellite and equatorial ion density and vertical plasma drift velocity observations with and without ESF activity obtained from the C/NOFS satellite are used to investigate the effect of gravity waves (GW) on ESF. The horizontal and vertical wavelengths of ionospheric oscillations and GWs are estimated by applying wavelet analysis techniques. In addition, vertically propagating GWs that dissipate energy in the ionosphere-thermosphere system are investigated using the spectral analysis technique. We find that the vertical wavelength of GW, corresponding to dominant wavelet power, ranges from 12 to 31 km regardless of the conditions of the ionosphere; however, GWs with vertical wavelengths between about 1 to 13 km are found every day, saturated between 90 and 110 km at different longitudinal sectors. Filtering out vertical wavelengths above 13 km from temperature perturbations, ranges of zonal wavelengths of GW (i.e., from about 290 to 950 km) are found corresponding to irregular and non-irregular ionosphere. Similarly, corresponding to dominant oscillations, the zonal wavelength of ion density perturbations is found within 16 to 1520 km. Moreover, we find an excellent agreement among the median zonal wavelengths of GW for the cases of irregular and non-irregular ionosphere and ion density perturbations that are 518, 495, and 491 km, respectively. The results imply that seed perturbations due to GW with a vertical wavelength from about 1 to 13 km evolve to ion density irregularity and may be amplified due to post-sunset vertical upward drift velocity.

3D Simulations Capture the Persistent Low-Mode Asymmetries Evident in Laser-Direct-Drive Implosions on OMEGA.

Spherical implosions in inertial confinement fusion are inherently sensitive to perturbations that may arise from experimental constraints and errors. Control and mitigation of low-mode (long wavelength) perturbations is a key milestone to improving implosion performances. We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer. Simulations match bang times, yields (separately accounting for laser-induced high modes and fuel age), hot spot flow velocities and direction, for which polarized crossed-beam energy transfer contributes to the systematic flow orientation evident in the OMEGA implosion database. Current levels of beam mispointing, imbalance, target offset, and asymmetry from polarized crossed-beam energy transfer degrade yields by more than 40%. The effectiveness of two mitigation strategies for low modes is explored.

Shock-driven dispersal of a corrugated finite-thickness particle layer

A research area emerging in the multiphase flow community is the study of shock-driven multiphase instability (SDMI), a gas–particle analog of the traditional fluid-fluid Richtmyer–Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian–Lagrangian approach. One objective of this study is to compare the simulated particle curtains to a comparable set of shock tube experiments performed to analyze traditional RMI of a gas curtain. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while also matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. Varying particle diameters are tested in the simulations to explore the impact of particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of the multiphase Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that the comparison depends on the diameter of the particles (thus, dependent on the Stokes number of the flow). A second objective of this study is to analyze the effect of the initial particle volume fraction on the evolution of the curtain and the behavior of the instability. This is done through analyzing the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.

Non-Gaussianity constraints with anisotropic μ distortion measurements from Planck

ABSTRACT Primordial non-Gaussianity can source μ-distortion anisotropies that are correlated with the large-scale temperature and polarization signals of the cosmic microwave background (CMB). A measurement of μT and μE correlations can therefore be used to constrain it on wavelengths of perturbations not directly probed by the standard CMB anisotropies. We carry out a first rigorous search for μ-distortion anisotropies with Planck data, applying the well-tested constrained ILC component-separation method combined with the needlet framework. We correlate the reconstructed μ map with the CMB anisotropies to derive constraints on the amplitude fNL of the local form bispectrum, specifically on the squeezed configurations with effective wavenumbers $k_s \simeq {740}\, \mathrm{Mpc^{-1}}$ and $k_L \simeq {0.05}\, \mathrm{Mpc^{-1}}$, improving previously estimated constraints by more than an order of magnitude. This enhancement is owing to the fact that we are able to use the full multipole information by carefully controlling biases and systematic effects in the analysis. We also for the first time incorporate constraints from measurements of μE correlations, which further tighten the limits. A combination of the derived Planck μT and μE power spectra yields |fNL| ≲ 6800 (95 per cent c.l.) on this highly squeezed bispectrum. This is only ≃3 times weaker than the anticipated constraint from Litebird. Furthermore we show that a combination of Litebird with Planck can improve the expected future constraint by ${\simeq}20{{\%}}$. These limits can be used to constrain multifield inflation models and primordial black hole formation scenarios, thus providing a promising novel avenue forward in CMB cosmology.

Parameters of the Galactic Spiral Density Wave from Masers with Parallax Errors Less Than 10$$\boldsymbol{\%}$$

We have studied the kinematics of Galactic masers and radio stars with measured VLBI trigonometric parallaxes and proper motions. We have considered masers with relative trigonometric parallax errors less than 10\% and determined the Galactic rotation parameters from them. In particular, the linear rotation velocity of the Galaxy at the solar distance $R_0$ has been found to be $244.4\pm4.3$ km s$^{-1}$ (for the adopted $R_0=8.1\pm0.1$ kpc). We have performed a joint and separate spectral analysis of the radial, residual tangential, and vertical maser velocities. For example, from the vertical maser velocities we have estimated the velocity perturbation amplitude $f_W=5.2\pm1.5$ km s$^{-1}$ with the wavelength $\lambda_W=2.6\pm0.7$ kpc, arguing for the influence of the spiral density wave on the vertical stellar velocities. Based on 104 masers within 3 kpc of the Sun, as a result of the joint solution, we have estimated the radial, $f_R=6.7\pm1.1$ km s$^{-1}$, and tangential, $f_\theta=2.6\pm1.2$ km s$^{-1}$, velocity perturbations, the perturbation wavelength $\lambda=2.1\pm0.3$ kpc, and the Sun's phase in the Galactic spiral density wave $\chi_\odot=-148\pm15^\circ$. We have confirmed the presence of the Radcliffe wave in the spatial distribution of masers and radio stars belonging to the Local Arm.

Mitigating laser imprint with a foam overcoating

In direct-drive inertial confinement fusion, laser imprint can cause areal density perturbations on the target shell that seed the Rayleigh–Taylor instability and further degrade the implosion. To mitigate the effect of laser imprint, a foam overcoating layer outside the target shell has been suggested to increase the thermal smoothing of the conduction region (between the ablation front and the critical density surface) and mass ablation of the ablation front. In this paper, we use a two-dimensional radiation hydrodynamic code FLASH to investigate the laser imprint mitigation performance and find other physical mechanisms of foam overcoatings. First, radiation ablation dynamically modulates density distribution not only to increase the frequency of the perturbed ablation front oscillation but also to decrease the amplitude of the oscillation. Second, a larger length of the shocked compression region reduces the amplitude of the perturbed shock front oscillation. The areal density perturbations decrease with the decrease in the perturbations of the ablation front and shock front. Based on the abovementioned physical mechanisms, we propose the optimal ranges of foam parameters to mitigate laser imprint with the aid of dimensional analysis: the foam thickness is about two to three times that of the perturbation wavelength, and the foam density is about 1/2–3/2 times that of the critical density.

Jeans instability in an expanding universe with dissipation

Jeans instability is analyzed in an expanding universe within the framework of BGK model of the Boltzmann equation and Poisson equations. The background is characterized by a comoving Maxwellian distribution function and a spacetime Newtonian gravitational potential which satisfy the BGK model of the Boltzmann–Poisson equations without the necessity to invoke “Jeans swindle.” The perturbations of the distribution function and Newtonian gravitational potentials from their background states are represented by plane waves of small amplitudes and a differential equation for the density contrast is determined. The density contrast differential equation was solved numerically and it is shown: (i) Jeans instability is characterized by perturbation wavelengths larger than Jeans wavelength where the density contrast grows with time. The growth of the density contrast is less accentuated for the case where the particle collisions are considered due to an energy dissipation; (ii) for perturbation wavelengths smaller than Jeans wavelength the density contrast has an oscillatory behavior in time and the oscillations for the case where the collisions are taken into account fade away in time due to the energy dissipation.

Modulational instability of the coupled waves between magnetosonic wave and ion acoustic wave

Present paper studies the interaction between the high frequency magnetosonic wave and the ion acoustic wave which is excited by the high frequency magnetosonic wave due to the ponderomotive force. The dispersion relation and the growth rate of the perturbation wave are obtained. The instability region is given in the present paper. It is found that the growth rate depends on the background magnetic field, the frequency of the magnetosonic wave as well as the perturbation wave vector. The results show that the long wavelength perturbation wave which propagates perpendicular to the magnetic field is stable; the larger the plasma thermal pressure, the smaller the growth rate. Our results may be quite important in understanding magnetic turbulence in the laser plasma and astrophysical phenomenon.

Kinematics of the Galaxy from Young Open Star Clusters with Data from the Gaia EDR3 Catalogue

We have analyzed the kinematics of open star clusters (OSCs) with the proper motions and distances calculated by Hao et al. based on Gaia EDR3 data. The mean line-of-sight velocities are known for a number of clusters from this list. We show that the Galactic rotation parameters determined from samples of OSCs with various ages are in good agreement between themselves. The most interesting results have been obtained from a sample of 967 youngest OSCs with a mean age of 18 Myr. In particular, we have found the following parameters of the angular velocity of Galactic rotation using only their proper motions and distances: $\Omega_0 =28.01\pm0.15$ km s$^{-1}$ kpc$^{-1},$ $\Omega^{'}_0=-3.674\pm0.040$ km s$^{-1}$ kpc$^{-2},$ and $\Omega^{''}_0=0.565\pm0.023$ km s$^{-1}$ kpc$^{-3}$. The circular rotation velocity of the solar neighborhood around the Galactic center here is $V_0=226.9\pm3.1$ km s$^{-1}$ for the adopted Galactocentric distance of the Sun $R_0=8.1\pm0.1$ kpc. The parameters of the spiral density wave have been determined from the space velocities of 233 young clusters. The amplitudes of the radial and tangential velocity perturbations produced by the spiral density wave are $f_R=9.1\pm0.8$ km s$^{-1}$ and $f_\theta=4.6\pm1.2$ km s$^{-1}$, respectively; the perturbation wavelengths are $\lambda_R=3.3\pm0.5$ kpc and $\lambda_\theta=2.6\pm0.6$ kpc for the the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave has been found to be $(\chi_\odot)_R\approx-180^\circ$.

Mathematical modeling of dendrite growth in an Al–Ge alloy with convective flow

A theory of stable dendrite growth in an undercooled binary melt is developed for the case of intense convection. Conductive heat and mass transfer boundary conditions are replaced by convective conditions, where the flux of heat (or solute) is proportional to the temperature or concentration difference between the surface of the dendrite and far from it. The marginal mode of perturbation wavelengths is calculated using the linear morphological stability analysis. Combining this analysis with the solvability theory, we have derived a selection criterion that represents the first condition to define a combination of dendrite tip velocity and tip diameter. The second condition—the undercooling balance—is derived for intense convection. The theory under consideration determines the dendrite tip velocity and tip diameter for low undercooling. This convective theory is combined with the classical theory of dendritic growth (conductive boundary conditions), which is valid for moderate and high undercooling. Thus, the entire range of melt undercooling is covered. Our results are in good agreement with experiments on Al–Ge crystallization.

Emergent patterns and stable interfaces during radial displacement of a viscoelastic fluid

We explore the interfacial instability that results when a Newtonian fluid (a glycerol-water mixture, inner fluid) displaces a viscoelastic fluid (a dense cornstarch suspension, outer fluid) in a radial Hele-Shaw cell. As the ratio of viscosities of the inner and outer fluids is increased, side branched interfacial patterns are replaced by more stable interfaces that display proportionate growth and finger coalescence. We correlate the average finger spacing with the most dominant wavelength of interfacial instability, computed using a mathematical model that accounts for viscous fingering in miscible Hele-Shaw displacements. The model predictions on the role of viscosity ratio on finger spacing are in close agreement with the experimental observations. Our study lends insight into the significant contribution of the viscoelasticity of the outer fluid on the morphology and growth of interfacial patterns.