Length Scale Of Perturbation Research Articles

Magnetic buoyancy instability and the anelastic approximation: regime of validity and relationship with compressible and Boussinesq descriptions

Magnetic buoyancy instability, which is of astrophysical importance, results from the influence of magnetic pressure variations on the density of a fluid in a gravitational field. It is inherently a compressible phenomenon and is, as such, fully described by the equations of compressible magnetohydrodynamics (MHD). For analytical and computational reasons, it is often convenient to study compressible MHD within simpler, asymptotically consistent reduced systems; the two most widely used result from the Boussinesq and anelastic approximations. Within the standard Boussinesq approximation of MHD, leading to the equations of Boussinesq magnetoconvection, magnetic buoyancy is excluded. It can, however, be included by a rescaling of the basic-state variables and by making further assumptions about the perturbation length scales. Within the anelastic approximation, no special measures are taken to incorporate magnetic buoyancy. It is, however, a priori unclear as to whether this neglect is justified, particularly in the light of the Boussinesq results. Our aims here are thus twofold. The first is to formulate the relationship between descriptions of magnetic buoyancy in the compressible, anelastic and Boussinesq systems. In so doing, we show that, under both the anelastic and Boussinesq approximations, magnetic buoyancy can be included either through a combination of a weak field and strong gradient, or, conversely, a strong field and weak gradient. Each has its own asymptotically consistent reduction, with dedicated governing equations. Our second aim is to address, through a linear stability analysis, under which conditions the standard anelastic system provides a faithful representation of magnetic buoyancy instability. For completeness, we also formulate the energy principle of ideal MHD within the anelastic framework, and demonstrate the relation with its fully compressible counterpart.

Cosmological backreaction in higher-derivative gravity expansions

We calculate a general effective stress-energy tensor induced by cosmological inhomogeneity in effective theories of gravity where the action is Taylor-expandable in the Riemann tensor and covariant derivatives of the Riemann tensor. This is of interest as an effective fluid that might provide an alternative to the cosmological constant, but it also applies to gravitational waves. We use an adaptation of Green and Wald's weak-averaging framework, which averages over perturbations in the field equation where the perturbation length scales are small compared to the averaging scale. In this adaptation, the length scale of the effective theory, 1/M, is also taken to be small compared with the averaging scale. This ensures that the perturbation length scales remain in fixed proportion to the length scale of the effective theory as the cosmological averaging scale is taken to be large. We find that backreaction from higher-derivative terms in the effective action can continue to be important in the late universe, given a source of sufficiently high-frequency metric perturbations. This backreaction might also provide a window on exotic particle physics in the far ultraviolet.

Relaxation of low-angle grain boundary structure by climb of the constituent dislocations

We study the relaxation of perturbed low-angle tilt grain boundaries by climb of the constituent dislocations. Under the combined influence of the long-range effects due the Peach–Koehler force and vacancy diffusion, dislocation climb always stabilizes the grain boundaries on a time scale that is proportional to the square of the perturbation length scale and inversely proportional to the point defect diffusivity. This relaxation has a different nature from that of perturbed low-angle grain boundaries by dislocation glide, in which only the long-range Peach–Koehler force is important, leading to a perturbation relaxation time linearly proportional to the perturbation wavelength itself.

Modal interactions between a large-wavelength inclined interface and small-wavelength multimode perturbations in a Richtmyer-Meshkov instability.

The interaction of a small-wavelength multimodal perturbation with a large-wavelength inclined interface perturbation is investigated for the reshocked Richtmyer-Meshkov instability using three-dimensional simulations. The ares code, developed at Lawrence Livermore National Laboratory, was used for these simulations and a detailed comparison of simulation results and experiments performed at the Georgia Tech Shock Tube facility is presented first for code validation. Simulation results are presented for four cases that vary in large-wavelength perturbation amplitude and the presence of secondary small-wavelength multimode perturbations. Previously developed measures of mixing and turbulence quantities are presented that highlight the large variation in perturbation length scales created by the inclined interface and the multimode complex perturbation. Measures are developed for entrainment, and turbulence anisotropy that help to identify the effects of and competition between each perturbations type. It is shown through multiple measures that before reshock the flow processes a distinct memory of the initial conditions that is present in both large-scale-driven entrainment measures and small-scale-driven mixing measures. After reshock the flow develops to a turbulentlike state that retains a memory of high-amplitude but not low-amplitude large-wavelength perturbations. It is also shown that the high-amplitude large-wavelength perturbation is capable of producing small-scale mixing and turbulent features similar to the small-wavelength multimode perturbations.

The impacts of heterogeneous land surface fluxes on the diurnal cycle precipitation: A framework for improving the GCM representation of land‐atmosphere interactions

AbstractThe present study aims to investigate the modulation of the diurnal cycle precipitation by heterogeneous land surface fluxes. By combining the National Center for Atmospheric Research Community Land Model (CLM) and vector vorticity equation cloud‐resolving model (VVM), experiments are designed to understand the responses of diurnal convection to heterogeneous land surface forcings of various spatial scales and intensities. To delineate the land‐atmosphere interactions, a two‐step off‐line approach is adopted. First, the CLM is driven by observational atmospheric forcing with different characteristic length scales and magnitudes. While the surface fluxes from the CLM show no significant difference in the domain‐averaged values, their spatial distribution responds significantly to the precipitation heterogeneity. In the second step, the derived CLM surface fluxes are used to drive the VVM. Results show that the timing of precipitation accelerates with increasing magnitude of surface flux perturbation, while the mean and diurnal ranges of precipitation roughly remain the same. The larger perturbation magnitude enhances the boundary layer vertical kinetic energy, which advances the development of the boundary layer. On the other hand, the mean and diurnal ranges of precipitation increase significantly, and the timing of initial precipitation delays with increasing perturbation length scale. The inland breeze induced by the large patches of surface fluxes tends to enhance the mesoscale organization of deep convection, hence the stronger precipitation. The present results highlight the importance of taking heterogeneous land surface fluxes into consideration in future development of general circulation model convection parameterizations associated with land and atmosphere interactions.

Richtmyer–Meshkov instability for elastic–plastic solids in converging geometries

We present a detailed study of the interface instability that develops at the boundary between a shell of elastic–plastic material and a cylindrical core of confined gas during the inbound implosive motion generated by a shock-wave. The main instability in this configuration is the so-called Richtmyer–Meshkov instability that arises when the shock wave crosses the material interface. Secondary instabilities, such as Rayleigh–Taylor, due to the acceleration of the interface, and Kelvin–Helmholtz, due to slip between solid and fluid, arise as the motion progresses. The reflection of the shock wave at the axis and its second interaction with the material interface as the shock moves outbound, commonly known as re-shock, results in a second Richtmyer–Meshkov instability that potentially increases the growth rate of interface perturbations, resulting in the formation of a mixing zone typical of fluid–fluid configurations and the loss of the initial perturbation length scales. The study of this problem is of interest for achieving stable inertial confinement fusion reactions but its complexity and the material conditions produced by the implosion close to the axis prove to be challenging for both experimental and numerical approaches. In this paper, we attempt to circumvent some of the difficulties associated with a classical numerical treatment of this problem, such as element inversion in Lagrangian methods or failure to maintain the relationship between the determinant of the deformation tensor and the density in Eulerian approaches, and to provide a description of the different events that occur during the motion of the interface. For this purpose, a multi-material numerical solver for evolving in time the equations of motion for solid and fluid media in an Eulerian formalism has been implemented in a Cartesian grid. Equations of state are derived using thermodynamically consistent hyperelastic relations between internal energy and stresses. The resolution required for capturing the state of solid and fluid materials close to the origin is achieved by making use of adaptive mesh refinement techniques. Rigid-body rotations contained in the deformation tensor have been shown to have a negative effect on the accuracy of the method in extreme compression conditions and are removed by transforming the deformation tensor into a stretch tensor at each time step. With this methodology, the evolution of the interface can be tracked up to a point at which numerical convergence cannot be achieved due to the inception of numerical Kelvin–Helmholtz instabilities caused by slip between materials. From that point, only qualitative conclusions can be extracted from this analysis. The influence of different geometrical parameters, initial conditions, and material properties on the motion of the interface are investigated. Some major differences are found with respect to the better understood fluid–fluid case. For example, increasing the wave number of the interface perturbations leads to a second phase reversal of the interface (i.e., the first phase reversal of the interface naturally occurs due to the initial negative growth-rate of the instability as the shock wave transitions from the high-density material to the low-density one). This phenomenon is caused by the compressive effect of the converging geometry and the low density of the gas with respect to the solid, which allows for the formation of an incipient spike in the center of an already existing bubble. Multiple solid–gas density ratios are also considered. Results show that the motion of the interface asymptotically converges to the solid–vacuum case. When a higher initial density for the gas is considered, the growth rate of interface perturbations decreases and, in some situations, its sign may reverse, as the fluid becomes more dense than the solid due to having higher compressibility. Finally, the influence of the Mach number of the driving shock and the yield stress on the mixing-zone is examined. We find that the width of the mixing zone produced after the re-shock increases in proportion to the strength of the incident shock. An increased yield stress in the solid material makes the interface less unstable due to vorticity being carried away from the interface by shear waves and limits the generation of smaller length scales after the re-shock.

Size-dependent mechanical behavior of free-standing glassy polymer thin films

Abstract

Capillary-gravity waves on a liquid film of arbitrary depth: Analysis of the wave resistance

We discuss the wave resistance in the case of an externally perturbed viscous liquid film of arbitrary thickness. Emphasis is placed on the dependence of the wave resistance on the film thickness H, the length scale b characterizing the external perturbation, and its velocity V. In particular, the effectiveness of the mechanisms of capillary-gravity waves and the viscous dissipation localized in the vicinity of the perturbation are compared and discussed as functions of H and V. We show that, in general, the wave resistance is a nonmonotonous function of H with a maximum whose amplitude and position depend on b and V. In the case of small H the wave resistance depends on a parameter S proportional V/H(3). We find three different regimes of this parameter in which the wave resistance behaves like S(r) with the exponent r equal to 1, 1/3, and -1. These results are also obtained independently within the thin liquid film approximation. This allows us to assess the range of validity of the thin liquid film approximation in various cases, in particular its dependence on the perturbation length scale b.

Shear heating induced lithospheric-scale localization: Does it result in subduction?

Even though it is a well-established fact that the Earth is currently in a plate-tectonics mode, the question on how to “break” lithospheric plates and initiate subduction remains a matter of debate. Here we focus on shear heating as a potential mechanism to cause lithospheric shear localization and subsequent subduction initiation in oceanic plates. It is shown that shear heating under some conditions (i) facilitates the formation of a lithospheric-scale shear zone and (ii) is capable of stabilizing a lithospheric-scale shear zone, thus creating the necessary condition for subduction initiation to occur. Furthermore, we demonstrate that not only the localization process is of importance, but also the post-localization stage, where rapidly growing convective instabilities might prevent an incipient subduction zone from developing.We develop scaling laws for both the localization and the post-localization stages. In the case of lithospheric localization, the characteristic length scale equals a quarter of the dominant folding wavelength in the lithosphere, thus of the order of the competent layer thickness. This shows that oceanic lithosphere develops an intrinsic perturbation length scale that is largely independent of smaller-scale heterogeneities. We compare the subduction initiation potential of wet olivine and dry olivine rheologies and find that, for Earth-like conditions, a dry olivine rheology is more likely to result in subduction initiation. A large plate age does not always increase the potential for subduction initiation, as it increases the potential for convective instabilities to occur. Instead, an optimal plate age exists for shear heating induced subduction initiation, which is around 40Ma for a wet olivine rheology.

An experimental study of the effects of surface tension in homogenizing perturbations in melt fraction

Static annealing experiments were conducted on fine-grained samples of a partially molten, olivine-rich rock to explore the role of interfacial tension driven flow in redistributing melt within the sample. A sample of fine-grained olivine + 20% chromite was prepared with an initially homogeneously distributed melt fraction of 0.04. When this sample was deformed in torsion, the melt segregated into distinct melt-rich bands uniformly spaced throughout the sample, as demonstrated in prior studies. Portions of this sample were then statically annealed for different lengths of time to observe the homogenization of the melt distribution. The evolution of the melt distribution in experimental samples was compared to numerical models based on formulations for interfacial tension driven flow that do or do not incorporate the effects of dissolution/precipitation coupled with diffusive mass transfer of components of the solid phase through the liquid phase (dissolution/diffusion/precipitation). The results indicate that, at the grain size and perturbation length scales in these samples, dissolution/diffusion/precipitation in response to the chemical potential gradient arising from the curvature of solid–liquid phase boundaries at triple junctions plays a significant role in accommodating interfacial tension driven flow. These experiments provide a valuable test for theory and allow us to place constraints on the homogenization rate of perturbations in melt fraction in rocks with a relatively simple composition. The results contribute to increasing our understanding of the nature of melt-rich, high-permeability pathways that may facilitate melt extraction from the upper mantle.

A detailed view of filaments and sheets in the warm-hot intergalactic medium

Numerical simulations predict a considerable fraction of the missing baryons at redshift z ~ 0 resting in the so called warm-hot intergalactic medium (WHIM). The filaments and sheets of the WHIM have high temperatures 10^5 - 10^7 K) and a high degree of ionization while having only low to intermediate densities. The particular physical conditions of the WHIM structures, e.g. density and temperature profiles, velocity fields, are expected to leave their special imprint on spectroscopic observations. In order to get further insight into these conditions, we perform hydrodynamical simulations of the WHIM. Instead of analyzing large simulations of cosmological structure formation, we simulate particular well-defined structures and study the impact of different physical processes as well as of the scale dependencies. We start with the comprehensive study of the one-dimensional collapse (pancake) and examine the influence of radiative cooling, heating due to an UV background, and thermal conduction. We investigate the effect of small scale perturbations given according to the initial cosmological power spectrum. If the initial perturbation length scale L exceeds ~ 2 Mpc the collapse leads to shock confined structures. As a result of radiative cooling and of heating due to an UV background a relatively cold and dense core forms in the one-dimensional case. The properties of the core (extension, density, and temperature) are correlated with L. For larger L the core sizes are more concentrated. Thermal conduction enhances this trend and may even result in an evaporation of the core. Our estimates predict that a core may start to evaporate for perturbation lengths larger than L ~ 30 Mpc. The obtained detailed profiles for density and temperature for prototype WHIM structures allow for the determination of possible spectral signatures by the WHIM.

Neutron star oceans: Instability, mixing, and heat transport

Stability of the ocean of magnetic neutron stars is considered. We argued that the ocean is unstable if the temperature varies along the surface. The instability grows on a time scale ∼0.1−100 s depending on the lengthscale of perturbations and generates a weak turbulence. Turbulence can be responsible for mixing between the surface and deep ocean layers and can enhance heat transport in the surface region.

The role of hydrodynamic instability in flame-vortex interaction

The interaction between a flame and a vortex pair is investigated by a front-tracking numerical method,developed for multifluid flows, in which a sharp interface separates incompressible fluids of different densities and viscosities. It is shown that, in a weak vortical flow field, the initial vortex simply serves as an initiation agent for the onset of flame front hydrodynamic instability, which in turn dominates the evolution of flame wrinkling and postflame vorticity generation. The flame-generated vorticity (FGV) is of opposite sign of the incoming vortices and is due to the baroclinic torque formed by the density gradient across the flame and the pressure gradient along the wrinkled flame surface. The relevance of the hydrodynamic instability is further demonstrated by analyzing the flame dynamics with the instability mechanism suppressed by imposing a perturbation length scale with minute growth rate. For sufficiently strong vortices, however, results show that while flame wrinkling is dominated by the incoming vortices, the FGV is affected by the combined pressure gradients of the vortices as well as that of the hydrodynamic instability. In fact, the only situation in which the course of the incoming vortices is preserved is for flames with small thermal expansion and thereby weak hydrodynamic instability influences.

The Pressure Limitations on Flux Pile-up Reconnection

The problem of the plasma pressure limitations on the rapidity of flux pile-up magnetic reconnection is re-examined, following the claim made by Jardine and Allen (1998) that the limitations can be removed by relaxing the assumption of zero-vorticity two-dimensional plasma flows. It is shown that for a two-dimensional stagnation point flow with nonzero vorticity the magnetic merging rate cannot exceed the Sweet–Parker scaling in a low-beta plasma. The pressure limitation appears to be much less restrictive for weak three-dimensional flux pile-up, provided the perturbation length scale in the third dimension is much less than the global length scale. The actual reconnection rate in the latter case, however, is much lower than this upper estimate unless the current sheet width is also much less than the global scale.

Mechanism of energy transformations in shear magnetohydrodynamic flows

Evolution of slow magnetoacoustic perturbations is used to demonstrate a new mechanism of plane Couette flow shear energy transformation. The initial uniform magnetic field is considered to be directed along the unperturbed flow velocity. We find that the amplification of waves is nonordinary---it occurs in a limited time interval and is anomalously strong. The unusual behavior is manifested also by the fact that the characteristic length scale of perturbation diminishes down to the dissipative scales not only due to nonlinear cascade processes, but due to a linear drift in the [bold k] space as well.

Swing amplification of nonaxisymmetric perturbations in stars and gas in a sheared galactic disk

We present a study of the growth of local, nonaxisymmetric perturbations in gravitationally coupled stars and gas in a differentially rotating galactic disk. The stars and gas are treated as two isothermal fluids of different velocity dispersions, with the stellar velocity dispersion being greater than that for the gas. We examine the physical effects of inclusion of a low-velocity dispersion component (gas) on the growth of non-axisymmetric perturbations in both stars and gas, as done for the axisymmetric case by Jog & Solomon. The amplified perturbations in stars and gas constitute trailing, material, spiral features which may be identified with the local spiral features seen in all spiral galaxies. The formulation of the two-fluid equations closely follows the one-fluid treatment by Goldreich & Lynden-Bell. The local, linearized perturbation equations in the sheared frame are solved to obtain the results for a temporary growth via swing amplification. The problem is formulated in terms of five dimensionless parameters-namely, the Q-factors for stars and gas, respectively; the gas mass fraction; the shearing rate in the galactic disk; and the length scale of perturbation. By using the observed values of these parameters, we obtain the amplifications and the pitch angles for features in stars and gas for dynamically distinct cases, as applicable for different regions of spiral galaxies. A real galaxy consisting of stars and gas may display growth of nonaxisymmetric perturbations even when it is stable against axisymmetric perturbations and/or when either fluid by itself is stable against non-axisymmetric perturbations. Due to its lower velocity dispersion, the gas exhibits a higher amplification than do the stars, and the amplified gas features are slightly more tightly wound than the stellar features. When the gas contribution is high, the stellar amplification and the range of pitch angles over which it can occur are both increased, due to the gravitational coupling between the two fluids. Thus, the two-fluid scheme can explain the origin of the broad spiral arms in the underlying old stellar populations of galaxies, as observed by Schweizer and Elmegreen & Elmegreen. The arms are predicted to be broader in gas-rich galaxies, as is indeed seen for example in M33. In the linear regime studied here, the arm contrast is shown to increase with radius in the inner Galaxy, in agreement with observations of external galaxies by Schweizer. These results follow directly due to the inclusion of gas in the problem.