1,693 research outputs found
On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities
We demonstrate a close analogy between a viscoelastic medium and an
electrically conducting fluid containing a magnetic field. Specifically, the
dynamics of the Oldroyd-B fluid in the limit of large Deborah number
corresponds to that of a magnetohydrodynamic (MHD) fluid in the limit of large
magnetic Reynolds number. As a definite example of this analogy, we compare the
stability properties of differentially rotating viscoelastic and MHD flows. We
show that there is an instability of the Oldroyd-B fluid that is physically
distinct from both the inertial and elastic instabilities described previously
in the literature, but is directly equivalent to the magnetorotational
instability in MHD. It occurs even when the specific angular momentum increases
outwards, provided that the angular velocity decreases outwards; it derives
from the kinetic energy of the shear flow and does not depend on the curvature
of the streamlines. However, we argue that the elastic instability of
viscoelastic Couette flow has no direct equivalent in MHD.Comment: 21 pages, 3 figures, to be published in J. Fluid Mec
A self-sustaining nonlinear dynamo process in Keplerian shear flows
A three-dimensional nonlinear dynamo process is identified in rotating plane
Couette flow in the Keplerian regime. It is analogous to the hydrodynamic
self-sustaining process in non-rotating shear flows and relies on the
magneto-rotational instability of a toroidal magnetic field. Steady nonlinear
solutions are computed numerically for a wide range of magnetic Reynolds
numbers but are restricted to low Reynolds numbers. This process may be
important to explain the sustenance of coherent fields and turbulent motions in
Keplerian accretion disks, where all its basic ingredients are present.Comment: 4 pages, 7 figures, accepted for publication in Physical Review
Letter
Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid
We describe an instability of viscoelastic Couette-Taylor flow that is
directly analogous to the magnetorotational instability (MRI) in astrophysical
magnetohydrodynamics, with polymer molecules playing the role of magnetic field
lines. By determining the conditions required for the onset of instability and
the properties of the preferred modes, we distinguish it from the centrifugal
and elastic instabilities studied previously. Experimental demonstration and
investigation should be much easier for the viscoelastic instability than for
the MRI in a liquid metal. The analogy holds with the case of a predominantly
toroidal magnetic field such as is expected in an accretion disk and it may be
possible to access a turbulent regime in which many modes are unstable.Comment: 4 pages, 4 figures, to be published in Physical Review Letter
Robustly Unstable Eigenmodes of the Magnetoshearing Instability in Accretion Disk
The stability of nonaxisymmetric perturbations in differentially rotating
astrophysical accretion disks is analyzed by fully incorporating the properties
of shear flows. We verify the presence of discrete unstable eigenmodes with
complex and pure imaginary eigenvalues, without any artificial disk edge
boundaries, unlike Ogilvie & Pringle(1996)'s claim. By developing the
mathematical theory of a non-self-adjoint system, we investigate the nonlocal
behavior of eigenmodes in the vicinity of Alfven singularities at
omega_D=omega_A, where omega_D is the Doppler-shifted wave frequency and
omega_A=k_// v_A is the Alfven frequency. The structure of the spectrum of
discrete eigenmodes is discussed and the magnetic field and wavenumber
dependence of the growth rate are obtained. Exponentially growing modes are
present even in a region where the local dispersion relation theory claims to
have stable eigenvalues. The velocity field created by an eigenmode is
obtained, which explains the anomalous angular momentum transport in the
nonlinear stage of this stability.Comment: 11pages, 11figures, to be published in ApJ. For associated eps files,
see http://dino.ph.utexas.edu/~knoguchi
Evolution of Migrating Planets Undergoing Gas Accretion
We analyze the orbital and mass evolution of planets that undergo run-away
gas accretion by means of 2D and 3D hydrodynamic simulations. The disk torque
distribution per unit disk mass as a function of radius provides an important
diagnostic for the nature of the disk-planet interactions. We first consider
torque distributions for nonmigrating planets of fixed mass and show that there
is general agreement with the expectations of resonance theory. We then present
results of simulations for mass-gaining, migrating planets. For planets with an
initial mass of 5 Earth masses, which are embedded in disks with standard
parameters and which undergo run-away gas accretion to one Jupiter mass (Mjup),
the torque distributions per unit disk mass are largely unaffected by migration
and accretion for a given planet mass. The migration rates for these planets
are in agreement with the predictions of the standard theory for planet
migration (Type I and Type II migration). The planet mass growth occurs through
gas capture within the planet's Bondi radius at lower planet masses, the Hill
radius at intermediate planet masses, and through reduced accretion at higher
planet masses due to gap formation. During run-away mass growth, a planet
migrates inwards by only about 20% in radius before achieving a mass of ~1
Mjup. For the above models, we find no evidence of fast migration driven by
coorbital torques, known as Type III migration. We do find evidence of Type III
migration for a fixed mass planet of Saturn's mass that is immersed in a cold
and massive disk. In this case the planet migration is assumed to begin before
gap formation completes. The migration is understood through a model in which
the torque is due to an asymmetry in density between trapped gas on the leading
side of the planet and ambient gas on the trailing side of the planet.Comment: 26 pages, 29 figures. To appear in The Astrophysical Journal vol.684
(September 20, 2008 issue
Magnetohydrodynamic turbulence in warped accretion discs
Warped, precessing accretion discs appear in a range of astrophysical
systems, for instance the X-ray binary Her X-1 and in the active nucleus of
NGC4258. In a warped accretion disc there are horizontal pressure gradients
that drive an epicyclic motion. We have studied the interaction of this
epicyclic motion with the magnetohydrodynamic turbulence in numerical
simulations. We find that the turbulent stress acting on the epicyclic motion
is comparable in size to the stress that drives the accretion, however an
important ingredient in the damping of the epicyclic motion is its parametric
decay into inertial waves.Comment: to appear in the proceedings of the 20th Texas Symposium on
Relativistic Astrophysics, J. C. Wheeler & H. Martel (eds.
Global axisymmetric Magnetorotational Instability with density gradients
We examine global incompressible axisymmetric perturbations of a
differentially rotating MHD plasma with radial density gradients. It is shown
that the standard magnetorotational instability, (MRI) criterion drawn from the
local dispersion relation is often misleading. If the equilibrium magnetic
field is either purely axial or purely toroidal, the problem reduces to finding
the global radial eigenvalues of an effective potential. The standard Keplerian
profile including the origin is mathematically ill-posed, and thus any solution
will depend strongly on the inner boundary. We find a class of unstable modes
localized by the form of the rotation and density profiles, with reduced
dependence on boundary conditions.Comment: 22 pages, 5 figure
The response of a turbulent accretion disc to an imposed epicyclic shearing motion
We excite an epicyclic motion, whose amplitude depends on the vertical
position, , in a simulation of a turbulent accretion disc. An epicyclic
motion of this kind may be caused by a warping of the disc. By studying how the
epicyclic motion decays we can obtain information about the interaction between
the warp and the disc turbulence. A high amplitude epicyclic motion decays
first by exciting inertial waves through a parametric instability, but its
subsequent exponential damping may be reproduced by a turbulent viscosity. We
estimate the effective viscosity parameter, , pertaining to
such a vertical shear. We also gain new information on the properties of the
disc turbulence in general, and measure the usual viscosity parameter,
, pertaining to a horizontal (Keplerian) shear. We find that,
as is often assumed in theoretical studies, is approximately
equal to and both are much less than unity, for the field
strengths achieved in our local box calculations of turbulence. In view of the
smallness () of and we conclude
that for the timescale for diffusion
or damping of a warp is much shorter than the usual viscous timescale. Finally,
we review the astrophysical implications.Comment: 12 pages, 18 figures, MNRAS accepte
Turbulence and angular momentum transport in a global accretion disk simulation
The global development of magnetohydrodynamic turbulence in an accretion disk
is studied within a simplified disk model that omits vertical stratification.
Starting with a weak vertical seed field, a saturated state is obtained after a
few tens of orbits in which the energy in the predominantly toroidal magnetic
field is still subthermal. The efficiency of angular momentum transport,
parameterized by the Shakura-Sunyaev alpha parameter, is of the order of 0.1.
The dominant contribution to alpha comes from magnetic stresses, which are
enhanced by the presence of weak net vertical fields. The power spectra of the
magnetic fields are flat or decline only slowly towards the largest scales
accessible in the calculation, suggesting that the viscosity arising from MHD
turbulence may not be a locally determined quantity. I discuss how these
results compare with observationally inferred values of alpha, and possible
implications for models of jet formation.Comment: ApJ Letters, in press. The paper and additional visualizations are
available at http://www.cita.utoronto.ca/~armitage/global_abs.htm
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