MAGNETIC COLLIMATION AND MAGNETOHYDRODYNAMIC KINK INSTABILITY DRIVEN BY DIFFERENTIAL ROTATION

2008 ◽  
Vol 17 (10) ◽  
pp. 1707-1713 ◽  
Author(s):  
C. S. CAREY ◽  
C. R. SOVINEC ◽  
S. HEINZ ◽  
J. E. EVERETT
Keyword(s):  
Growth Rate ◽  
Accretion Disk ◽  
Differential Rotation ◽  
Rotation Rate ◽  
Three Dimensional ◽  
Small Scale ◽  
Two Dimensional ◽  
Extragalactic Jets ◽  
Magnetohydrodynamic Simulations ◽  
Kink Instability

We investigate the launching and stability of extragalactic jets through magnetohydrodynamic simulations of jet evolution. In these simulations, a small scale equilibrium magnetic corona is twisted by a differentially rotating accretion disk. Two-dimensional calculations show the formation of a collimated outflow. This outflow is divided into two regions by the Alfvén surface: a magnetically dominated Poynting region, and a kinetically dominated region. Three-dimensional calculations show that the outflow is unstable to the m = 1 kink instability, and that the growth rate of the kink instability decreases as the rotation rate of the accretion disk increases.

scholarly journals CURRENT DRIVEN KINK INSTABILITY IN A MAGNETICALLY DOMINATED ROTATING RELATIVISTIC JET

2014 ◽  
Vol 28 ◽  
pp. 1460201 ◽  
Author(s):  
YOSUKE MIZUNO ◽  
KEN-ICHI NISHIKAWA ◽  
YURI LYUBARSKY ◽  
PHILIP E. HARDEE
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Three Dimensional ◽  
Temporal Development ◽  
Differential Motion ◽  
Relativistic Jet ◽  
Linear And Nonlinear ◽  
Magnetohydrodynamic Simulations ◽  
Kink Instability ◽  
Helical Magnetic Field

We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via three-dimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. In the rotating relativistic jet case, developing helical kink structure propagates along jet as it grows in amplitude. The growth rate of the CD kink instability does not depend on the jet rotation. The coupling of multiple unstable wavelengths is crucial to determining whether the jet is eventually disrupted in the nonlinear stage. The CD kink instability deformed magnetic field may trigger magnetic reconnection in the jet.

scholarly journals Turbulence in the Atmosphere of B-Type Stars

1980 ◽  
Vol 51 ◽  
pp. 170-171
Author(s):  
Keiichi Kodaira
Keyword(s):  
Surface Layer ◽  
Velocity Field ◽  
Differential Rotation ◽  
Meridional Circulation ◽  
Three Dimensional ◽  
Scale Height ◽  
Small Scale ◽  
Two Dimensional ◽  
Viscosity Term ◽  
Pressure Scale

AbstractThe stationary turbulent surface layer, whose depth is of the order of the pressure scale height in the subphotospheric layer, was investigated for B-type stars, using the momentum and the continuity equations with the inertia term neglected but the turbulence-viscosity term included. The mean velocity field is dominated by the horizontal component of the meridional circulation, driven by the pressure-density unbalance in the radiative envelope of the rotating star, and the differential rotation induced by the Coriolis force.The model calculation for a B3IV-V star with the equatorial rotational velocity of 200 km/s led to the conclusions that the velocity field due to the differential rotation is of the order of 0.1-1 km/s, the velocity field of the meridional circulation itself is negligible, the velocity field of the three-dimensional shear turbulence is of the order of 0.1 km/s, and i t s scale is comparable to or less than the pressure scale height, the velocity field of the horizontal two-dimensional turbulence is of the order of 1-10 km/s, and i t s maximum scale ranges from a few times the pressure scale height to one-fiftieth of the stellar radius. If the index of the energy density law is close to 3.5, the turbulent surface layer may be dominated by the large scale (two-dimensional) barotropic eddies whose energy is fed by the small scale (three-dimensional) baroclinic turbulence in a way similar to the planetary atmospheres. In this case we may expect the tangential macroturbulence of the order of 1-10 km/s, though the interaction between this and the small-scale three-dimensional turbulence still remains to be investigated.

MAGNETIC FIELD AMPLIFICATION BY RELATIVISTIC SHOCKS IN AN INHOMOGENEOUS MEDIUM

2012 ◽  
Vol 08 ◽  
pp. 364-367
Author(s):  
YOSUKE MIZUNO ◽  
MARTIN POHL ◽  
JACEK NIEMIEC ◽  
BING ZHANG ◽  
KEN-ICHI NISHIKAWA ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Inhomogeneous Medium ◽  
Magnetic Energy ◽  
Small Scale ◽  
Two Dimensional ◽  
Filamentary Structure ◽  
Field Amplification ◽  
Relativistic Shocks ◽  
Field Lines ◽  
Magnetohydrodynamic Simulations

We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that the so-called small-scale dynamo is occurring in the postshock region. We also find that the amplitude of magnetic-field amplification depends on the direction of the mean preshock magnetic field.

A RHEED Study of MBE Growth of ZnSe on GaAs (111) A-(2 × 2)

2003 ◽  
Vol 10 (04) ◽  
pp. 669-675
Author(s):  
F. S. Gard ◽  
J. D. Riley ◽  
R. Leckey ◽  
B. F. Usher
Keyword(s):  
Growth Rate ◽  
Electron Diffraction ◽  
Substrate Temperature ◽  
Three Dimensional ◽  
High Energy ◽  
Growth Mode ◽  
Two Dimensional ◽  
High Energy Electron ◽  
Mbe Growth ◽  
Atomic Flux

ZnSe epilayers have been grown under various Se/Zn atomic flux ratios in the range of 0.22–2.45 at a substrate temperature of 350°C on Zn pre-exposed GaAs (111) A surfaces. Real time reflection high energy electron diffraction (RHEED) observations have shown a transition from a two-dimensional (2D) to a three-dimensional (3D) growth mode. The transition time depends directly upon the growth rate. A detailed discussion is presented to explore the cause of this change in the growth mode.

The anatomy of the mixing transition in homogeneous and stratified free shear layers

2000 ◽  
Vol 413 ◽  
pp. 1-47 ◽  
Author(s):  
C. P. CAULFIELD ◽  
W. R. PELTIER
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Small Scale ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Free Shear Layers ◽  
Nonlinear Amplification

We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free shear layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable sublayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of shear layer evolution, with the flow Reynolds number (defined on the basis of shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified shear layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified shear layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.

scholarly journals Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities

1994 ◽  
Vol 12 (4) ◽  
pp. 725-750 ◽  
Author(s):  
D.L. Youngs
Keyword(s):  
Numerical Simulation ◽  
Turbulence Model ◽  
Turbulent Mixing ◽  
Inertial Confinement Fusion ◽  
Three Dimensional ◽  
Small Scale ◽  
Inertial Confinement ◽  
Two Dimensional ◽  
Confinement Fusion ◽  
Icf Target

Rayleigh-Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at the pusher–fuel interface in inertial confinement fusion (ICF) targets may significantly degrade thermonuclear burn. Present-day supercomputers may be used to understand the fundamental instability mechanisms and to model the effect of the ensuing mixing on the performance of the ICF target. Direct three-dimensional numerical simulation is used to investigate turbulent mixing due to RT and RM instability in simple situations. A two-dimensional turbulence model is used to assess the effect of small-scale turbulent mixing in the axisymmetric implosion of an idealized ICF target.

Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations

2002 ◽  
Vol 451 ◽  
pp. 261-282 ◽  
Author(s):  
F. GRAF ◽  
E. MEIBURG ◽  
C. HÄRTEL
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Linear Stability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interface Thickness ◽  
Gap Width ◽  
Stability Results ◽  
Hele Shaw Cell

We consider the situation of a heavier fluid placed above a lighter one in a vertically arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this configuration, experiments and nonlinear simulations recently reported by Fernandez et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on the order of five times the gap width. These findings are in disagreement with linear stability results based on the gap-averaged Hele-Shaw approach, which predict much smaller wavelengths. Similar observations have been made for immiscible flows as well (Maxworthy 1989).In order to resolve the above discrepancy, we perform a linear stability analysis based on the full three-dimensional Stokes equations. A generalized eigenvalue problem is formulated, whose numerical solution yields both the growth rate and the two-dimensional eigenfunctions in the cross-gap plane as functions of the spanwise wavenumber, an ‘interface’ thickness parameter, and Ra. For large Ra, the dispersion relations confirm that the optimally amplified wavelength is about five times the gap width, with the exact value depending on the interface thickness. The corresponding growth rate is in very good agreement with the experimental data as well. The eigenfunctions indicate that the predominant fluid motion occurs within the plane of the Hele-Shaw cell. However, for large Ra purely two-dimensional modes are also amplified, for which there is no motion in the spanwise direction. Scaling laws are provided for the dependence of the maximum growth rate, the corresponding wavenumber, and the cutoff wavenumber on Ra and the interface thickness. Furthermore, the present results are compared both with experimental data, as well as with linear stability results obtained from the Hele-Shaw equations and a modified Brinkman equation.

Small-scale structure of two-dimensional magnetohydrodynamic turbulence

1979 ◽  
Vol 90 (1) ◽  
pp. 129-143 ◽  
Author(s):  
Steven A. Orszag ◽  
Cha-Mei Tang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Three Dimensional ◽  
Scale Structure ◽  
Magnetohydrodynamic Flow ◽  
Small Scale ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Hydrodynamic Turbulence ◽  
Small Scale Structure

The formation of singularities in two-dimensional magnetohydrodynamic flow is investigated by direct numerical simulation. It is shown that two-dimensional magnetohydrodynamic turbulence is not as singular as three-dimensional hydrodynamic turbulence (in the sense that it has a less highly excited small-scale structure) but that it is more singular than two-dimensional hydrodynamic turbulence.

Secondary instability of a temporally growing mixing layer

1987 ◽  
Vol 184 ◽  
pp. 207-243 ◽  
Author(s):  
Ralph W. Metcalfe ◽  
Steven A. Orszag ◽  
Marc E. Brachet ◽  
Suresh Menon ◽  
James J. Riley
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Mixing Layers ◽  
Navier Stokes ◽  
Small Scale ◽  
Two Dimensional ◽  
Mean Flow ◽  
Direct Numerical Integration

The three-dimensional stability of two-dimensional vortical states of planar mixing layers is studied by direct numerical integration of the Navier-Stokes equations. Small-scale instabilities are shown to exist for spanwise scales at which classical linear modes are stable. These modes grow on convective timescales, extract their energy from the mean flow and exist at moderately low Reynolds numbers. Their growth rates are comparable with the most rapidly growing inviscid instability and with the growth rates of two-dimensional subharmonic (pairing) modes. At high amplitudes, they can evolve into pairs of counter-rotating, streamwise vortices, connecting the primary spanwise vortices, which are very similar to the structures observed in laboratory experiments. The three-dimensional modes do not appear to saturate in quasi-steady states as do the purely two-dimensional fundamental and subharmonic modes in the absence of pairing. The subsequent evolution of the flow depends on the relative amplitudes of the pairing modes. Persistent pairings can inhibit three-dimensional instability and, hence, keep the flow predominantly two-dimensional. Conversely, suppression of the pairing process can drive the three-dimensional modes to more chaotic, turbulent-like states. An analysis of high-resolution simulations of fully turbulent mixing layers confirms the existence of rib-like structures and that their coherence depends strongly on the presence of the two-dimensional pairing modes.

Void growth in shear

1986 ◽  
Vol 407 (1833) ◽  
pp. 435-458 ◽  
Keyword(s):  
Growth Rate ◽  
Strain Rate ◽  
Void Growth ◽  
Three Dimensional ◽  
Shape Evolution ◽  
Two Dimensional ◽  
Simple Shearing ◽  
Hydrostatic Tension ◽  
Dilatation Rate ◽  
Approximate Formulas

The growth of an isolated void is analysed for a void contained in a block of material undergoing simple shearing combined with superimposed hydrostatic tension. The evolution of the size, shape and orientation of two- and three-dimensional voids in an incompressible, linearly viscous solid is first discussed. The main problem addressed is the behaviour of a two-dimensional cylindrical void in an incompressible, nonlinearly viscous solid for which the strain rate varies as the stress to a power. The growth rate of the void and its shape evolution are strong functions of the degree of material nonlinearity. Relatively simple approximate formulas are obtained for the dilatation rate of a circular void as well as for the void potential. The constitutive relation of a block of material containing a dilute distribution of circular cylindrical voids is obtained directly using the isolated void potential. The paper concludes with a summary of available results for the dilatation rates of voids and cracks under combinations of shear and hydrostatic tension.

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