92 research outputs found
Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit
Angular momentum transport in accretion discs is often believed to be due to
magnetohydrodynamic turbulence mediated by the magnetorotational instability.
Despite an abundant literature on the MRI, the parameters governing the
saturation amplitude of the turbulence are poorly understood and the existence
of an asymptotic behavior in the Ohmic diffusion regime is not clearly
established. We investigate the properties of the turbulent state in the small
magnetic Prandtl number limit. Since this is extremely computationally
expensive, we also study the relevance and range of applicability of the most
common subgrid scale models for this problem. Unstratified shearing boxes
simulations are performed both in the compressible and incompressible limits,
with a resolution up to 800 cells per disc scale height. The latter constitutes
the largest resolution ever attained for a simulation of MRI turbulence. In the
presence of a mean magnetic field threading the domain, angular momentum
transport converges to a finite value in the small Pm limit. When the mean
vertical field amplitude is such that {\beta}, the ratio between the thermal
and magnetic pressure, equals 1000, we find {\alpha}~0.032 when Pm approaches
zero. In the case of a mean toroidal field for which {\beta}=100, we find
{\alpha}~0.018 in the same limit. Both implicit LES and Chollet-Lesieur closure
model reproduces these results for the {\alpha} parameter and the power
spectra. A reduction in computational cost of a factor at least 16 (and up to
256) is achieved when using such methods. MRI turbulence operates efficiently
in the small Pm limit provided there is a mean magnetic field. Implicit LES
offers a practical and efficient mean of investigation of this regime but
should be used with care, particularly in the case of a vertical field.
Chollet-Lesieur closure model is perfectly suited for simulations done with a
spectral code.Comment: Accepted for publication in A&
Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow
The magnetorotational (MRI) dynamo has long been considered one of the
possible drivers of turbulent angular momentum transport in astrophysical
accretion disks. However, various numerical results suggest that this dynamo
may be difficult to excite in the astrophysically relevant regime of magnetic
Prandtl number (Pm) significantly smaller than unity, for reasons currently not
well understood. The aim of this article is to present the first results of an
ongoing numerical investigation of the role of both linear and nonlinear
dissipative effects in this problem. Combining a parametric exploration and an
energy analysis of incompressible nonlinear MRI dynamo cycles representative of
the transitional dynamics in large aspect ratio shearing boxes, we find that
turbulent magnetic diffusion makes the excitation and sustainment of this
dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for
decreasing Pm. This results in an increase in the critical Rm of the dynamo for
increasing kinematic Reynolds number (Re), in agreement with earlier numerical
results. Given its very generic nature, we argue that turbulent magnetic
diffusion could be an important determinant of MRI dynamo excitation in disks,
and may also limit the efficiency of angular momentum transport by MRI
turbulence in low Pm regimes.Comment: 7 pages, 6 figure
Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?
In Keplerian accretion disks, turbulence and magnetic fields may be jointly
excited through a subcritical dynamo process involving the magnetorotational
instability (MRI). High-resolution simulations exhibit a tendency towards
statistical self-organization of MRI dynamo turbulence into large-scale cyclic
dynamics. Understanding the physical origin of these structures, and whether
they can be sustained and transport angular momentum efficiently in
astrophysical conditions, represents a significant theoretical challenge. The
discovery of simple periodic nonlinear MRI dynamo solutions has recently proven
useful in this respect, and has notably served to highlight the role of
turbulent magnetic diffusion in the seeming decay of the dynamics at low
magnetic Prandtl number Pm (magnetic diffusivity larger than viscosity), a
common regime in accretion disks. The connection between these simple
structures and the statistical organization reported in turbulent simulations
remained elusive, though. Here, we report the numerical discovery in moderate
aspect ratio Keplerian shearing boxes of new periodic, incompressible,
three-dimensional nonlinear MRI dynamo solutions with a larger dynamical
complexity reminiscent of such simulations. These "chimera" cycles are
characterized by multiple MRI-unstable dynamical stages, but their basic
physical principles of self-sustainment are nevertheless identical to those of
simpler cycles found in azimuthally elongated boxes. In particular, we find
that they are not sustained at low Pm either due to subcritical turbulent
magnetic diffusion. These solutions offer a new perspective into the transition
from laminar to turbulent instability-driven dynamos, and may prove useful to
devise improved statistical models of turbulent accretion disk dynamos.Comment: 12 pages, 8 figures, submitted to A&
A procedure to analyze nonlinear density waves in Saturn's rings using several occultation profiles
Cassini radio science experiments have provided multiple occultation optical
depth profiles of Saturn's rings that can be used in combination to analyze
density waves. This paper establishes an accurate procedure of inversion of the
wave profiles to reconstruct the wave kinematic parameters as a function of
semi-major axis, in the nonlinear regime. This procedure is achieved from
simulated data in the presence of realistic noise perturbations, to control the
reconstruction error. By way of illustration we have applied our procedure to
the Mimas 5:3 density wave. We were able to recover precisely the kinematic
parameters from the radio experiment occultation data in most of the
propagation region; a preliminary analysis of the pressure-corrected dispersion
allowed us to determine new but still uncertain values for the opacity
( cm/g) and velocity dispersion of ( cm/s) in
the wave region. Our procedure constitutes the first step in our planned
analysis of the density waves of Saturn's rings. It is very accurate and
efficient in the far-wave region. However, improvements are required within the
first wavelength. The ways in which this method can be used to establish
diagnostics of ring physics are outlined.Comment: 50 pages,13 figures, 2 tables. Published in Icarus
Nonlinear energy transfers in accretion discs MRI turbulence. I-Net vertical field case
The magnetorotational instability (MRI) is believed to be responsible for
most of the angular momentum transport in accretion discs. However, molecular
dissipation processes may drastically change the efficiency of MRI turbulence
in realistic astrophysical situations. The physical origin of this dependency
is still poorly understood as linear and quasi linear theories fail to explain
it. In this paper, we look for the link between molecular dissipation processes
and MRI transport of angular momentum in non stratified shearing box
simulations including a mean vertical field. We show that magnetic helicity is
unimportant in the model we consider. We perform a spectral analysis on the
simulations tracking energy exchanges in spectral space when turbulence is
fully developed. We find that the energy exchanges are essentially direct (from
large to small scale) whereas some non linear interactions appear to be non
local in spectral space. We speculate that these non local interactions are
responsible for the correlation between turbulent transport and molecular
dissipation. We argue that this correlation should then disappear when a
significant scale separation is achieved and we discuss several methods by
which one can test this hypothesis.Comment: 10 pages, 9 figures, accepted for publication in Astronomy &
Astrophysic
On the Phenomenology of Hydrodynamic Shear Turbulence
The question of a purely hydrodynamic origin of turbulence in accretion disks
is reexamined, on the basis of a large body of experimental and numerical
evidence on various subcritical (i.e., linearly stable) hydrodynamic flows.
One of the main points of this paper is that the length scale and velocity
fluctuation amplitude which are characteristic of turbulent transport in these
flows scale like , where is the minimal Reynolds number for
the onset of fully developed turbulence. From this scaling, a simple
explanation of the dependence of with relative gap width in subcritical
Couette-Taylor flows is developed. It is also argued that flows in the shearing
sheet limit should be turbulent, and that the lack of turbulence in all such
simulations performed to date is most likely due to a lack of resolution, as a
consequence of the effect of the Coriolis force on the large scale fluctuations
of turbulent flows.
These results imply that accretion flows should be turbulent through
hydrodynamic processes. If this is the case, the Shakura-Sunyaev
parameter is constrained to lie in the range in accretion
disks, depending on unknown features of the mechanism which sustains
turbulence. Whether the hydrodynamic source of turbulence is more efficient
than the MHD one where present is an open question.Comment: 31 pages, 3 figures. Accepted for publication in Ap
Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows
The nature of dynamo action in shear flows prone to magnetohydrodynamic
instabilities is investigated using the magnetorotational dynamo in Keplerian
shear flow as a prototype problem. Using direct numerical simulations and
Newton's method, we compute an exact time-periodic magnetorotational dynamo
solution to the three-dimensional dissipative incompressible
magnetohydrodynamic equations with rotation and shear. We discuss the physical
mechanism behind the cycle and show that it results from a combination of
linear and nonlinear interactions between a large-scale axisymmetric toroidal
magnetic field and non-axisymmetric perturbations amplified by the
magnetorotational instability. We demonstrate that this large scale dynamo
mechanism is overall intrinsically nonlinear and not reducible to the standard
mean-field dynamo formalism. Our results therefore provide clear evidence for a
generic nonlinear generation mechanism of time-dependent coherent large-scale
magnetic fields in shear flows and call for new theoretical dynamo models.
These findings may offer important clues to understand the transitional and
statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review
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