skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field

Abstract

We investigate magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI) in Keplerian disks with a nonzero net azimuthal magnetic field using shearing box simulations. As distinct from previous studies, we analyze turbulence dynamics in Fourier ($${\boldsymbol{k}}$$-) space to understand its sustenance. The linear growth of the MRI with the azimuthal field has a transient character and is anisotropic in Fourier space, leading to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a new type of angular redistribution of modes in Fourier space—the nonlinear transverse cascade—rather than the usual direct/inverse cascade. Here, we demonstrate that the turbulence is sustained by the interplay of the linear transient growth of the MRI (which is the only energy supply for the turbulence) and the transverse cascade. These two processes operate at large length scales, comparable to the box size (disk scale height); the corresponding small wavenumber area, called the vital area in Fourier space, is crucial for the sustenance, while outside the vital area, direct cascade dominates. The interplay of the linear and nonlinear processes in Fourier space is generally too intertwined for a vivid schematization. Nevertheless, we reveal the basic subcycle of the sustenance that clearly shows the synergy of these processes in the self-organization of the magnetized flow system. This synergy is quite robust and persists for the considered different aspect ratios of the simulation boxes. The spectral characteristics of the dynamical processes in these boxes are qualitatively similar, indicating the universality of the sustenance mechanism of the MRI turbulence.

Authors:
 [1]; ORCiD logo [2];  [3];  [4]; ORCiD logo [5]
  1. Univ. of Texas, Austin, TX (United States). Dept. of Physics
  2. Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Tbilisi State Univ., Tbilisi (Georgia). Dept. of Physics, Faculty of Exact and Natural Sciences; Ilia State Univ., Tbilisi (Georgia). Abastumani Astrophysical Observatory
  3. Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies and Space and Geophysics Lab.
  4. Ilia State Univ., Tbilisi (Georgia). Abastumani Astrophysical Observatory; Tbilisi State Univ., Tbilisi (Georgia). Inst. of Geophysics
  5. INAF/Osservatorio Astrofisico di Torino, Pino Torinese (Italy). Strada Osservatorio
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1537191
Grant/Contract Number:  
FG02-04ER54742
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 845; Journal Issue: 1; Journal ID: ISSN 1538-4357
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; astronomy & astrophysics; accretion; accretion disks; instabilities; magnetohydrodynamics (MHD); turbulence

Citation Formats

Gogichaishvili, D., Mamatsashvili, G., Horton, W., Chagelishvili, G., and Bodo, G. Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field. United States: N. p., 2017. Web. doi:10.3847/1538-4357/aa7ed1.
Gogichaishvili, D., Mamatsashvili, G., Horton, W., Chagelishvili, G., & Bodo, G. Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field. United States. doi:10.3847/1538-4357/aa7ed1.
Gogichaishvili, D., Mamatsashvili, G., Horton, W., Chagelishvili, G., and Bodo, G. Thu . "Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field". United States. doi:10.3847/1538-4357/aa7ed1. https://www.osti.gov/servlets/purl/1537191.
@article{osti_1537191,
title = {Nonlinear Transverse Cascade and Sustenance of MRI Turbulence in Keplerian Disks with an Azimuthal Magnetic Field},
author = {Gogichaishvili, D. and Mamatsashvili, G. and Horton, W. and Chagelishvili, G. and Bodo, G.},
abstractNote = {We investigate magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI) in Keplerian disks with a nonzero net azimuthal magnetic field using shearing box simulations. As distinct from previous studies, we analyze turbulence dynamics in Fourier (${\boldsymbol{k}}$-) space to understand its sustenance. The linear growth of the MRI with the azimuthal field has a transient character and is anisotropic in Fourier space, leading to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a new type of angular redistribution of modes in Fourier space—the nonlinear transverse cascade—rather than the usual direct/inverse cascade. Here, we demonstrate that the turbulence is sustained by the interplay of the linear transient growth of the MRI (which is the only energy supply for the turbulence) and the transverse cascade. These two processes operate at large length scales, comparable to the box size (disk scale height); the corresponding small wavenumber area, called the vital area in Fourier space, is crucial for the sustenance, while outside the vital area, direct cascade dominates. The interplay of the linear and nonlinear processes in Fourier space is generally too intertwined for a vivid schematization. Nevertheless, we reveal the basic subcycle of the sustenance that clearly shows the synergy of these processes in the self-organization of the magnetized flow system. This synergy is quite robust and persists for the considered different aspect ratios of the simulation boxes. The spectral characteristics of the dynamical processes in these boxes are qualitatively similar, indicating the universality of the sustenance mechanism of the MRI turbulence.},
doi = {10.3847/1538-4357/aa7ed1},
journal = {The Astrophysical Journal (Online)},
number = 1,
volume = 845,
place = {United States},
year = {2017},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Dynamics of Protoplanetary Disks
journal, September 2011


Chaos transition despite linear stability
journal, November 1994


A mostly linear model of transition to turbulence
journal, April 1995

  • Baggett, Jeffrey S.; Driscoll, Tobin A.; Trefethen, Lloyd N.
  • Physics of Fluids, Vol. 7, Issue 4
  • DOI: 10.1063/1.868606

On the Anisotropic Nature of Mri-Driven Turbulence in Astrophysical Disks
journal, April 2015


On the stability of an accretion disc containing a toroidal magnetic field: the effect of resistivity
journal, June 1997

  • Papaloizou, J. C. B.; Terquem, C.
  • Monthly Notices of the Royal Astronomical Society, Vol. 287, Issue 4
  • DOI: 10.1093/mnras/287.4.771

Local Three-dimensional Magnetohydrodynamic Simulations of Accretion Disks
journal, February 1995

  • Hawley, John F.; Gammie, Charles F.; Balbus, Steven A.
  • The Astrophysical Journal, Vol. 440
  • DOI: 10.1086/175311

Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit
journal, July 2015


A study of the transient dynamics of perturbations in Keplerian discs using a variational approach
journal, June 2014

  • Zhuravlev, V. V.; Razdoburdin, D. N.
  • Monthly Notices of the Royal Astronomical Society, Vol. 442, Issue 1
  • DOI: 10.1093/mnras/stu848

Enhanced Angular Momentum Transport in Accretion Disks
journal, September 2003


On self-sustained dynamo cycles in accretion discs
journal, July 2008


Turbulence in global simulations of magnetized thin accretion discs: Turbulence in magnetized thin discs
journal, July 2011


On the Convergence of Magnetorotational Turbulence in Stratified Isothermal Shearing Boxes
journal, May 2014


Pseudospectra of the Orr–Sommerfeld Operator
journal, February 1993

  • Reddy, Satish C.; Schmid, Peter J.; Henningson, Dan S.
  • SIAM Journal on Applied Mathematics, Vol. 53, Issue 1
  • DOI: 10.1137/0153002

Locality of mhd Turbulence in Isothermal Disks
journal, March 2009


Turbulence in Weakly Ionized Protoplanetary Disks
journal, November 2012


Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes
journal, June 2013


Radially Extended, Stratified, Local Models of Isothermal Disks
journal, January 2011


Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
journal, January 1995

  • Goldreich, P.; Sridhar, S.
  • The Astrophysical Journal, Vol. 438
  • DOI: 10.1086/175121

The non-axisymmetric instability of a cylindrical shear flow containing an azimuthal magnetic field
journal, March 1996

  • Ogilvie, G. I.; Pringle, J. E.
  • Monthly Notices of the Royal Astronomical Society, Vol. 279, Issue 1
  • DOI: 10.1093/mnras/279.1.152

A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution
journal, July 1991

  • Balbus, Steven A.; Hawley, John F.
  • The Astrophysical Journal, Vol. 376
  • DOI: 10.1086/170270

Dynamic anisotropy in MHD turbulence induced by mean magnetic field
journal, February 2017

  • Sundar, Sita; Verma, Mahendra K.; Alexakis, Alexandros
  • Physics of Plasmas, Vol. 24, Issue 2
  • DOI: 10.1063/1.4975609

Viscous and Resistive Effects on the Magnetorotational Instability with a net Toroidal Field
journal, November 2009


Testing Convergence for Global Accretion Disks
journal, July 2013


Magnetohydrodynamic Shearing Waves
journal, May 2007

  • Johnson, Bryan M.
  • The Astrophysical Journal, Vol. 660, Issue 2
  • DOI: 10.1086/513867

The stress–pressure relationship in simulations of MRI-induced turbulence
journal, November 2015

  • Ross, Johnathan; Latter, Henrik N.; Guilet, Jerome
  • Monthly Notices of the Royal Astronomical Society, Vol. 455, Issue 1
  • DOI: 10.1093/mnras/stv2286

The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks
journal, February 2000

  • Fleming, Timothy P.; Stone, James M.; Hawley, John F.
  • The Astrophysical Journal, Vol. 530, Issue 1
  • DOI: 10.1086/308338

Revisiting linear dynamics of non-axisymmetric perturbations in weakly magnetized accretion discs
journal, September 2013

  • Mamatsashvili, G. R.; Chagelishvili, G. D.; Bodo, G.
  • Monthly Notices of the Royal Astronomical Society, Vol. 435, Issue 3
  • DOI: 10.1093/mnras/stt1470

Sustained Magnetorotational Turbulence in Local Simulations of Stratified Disks with zero net Magnetic flux
journal, March 2010

  • Davis, Shane W.; Stone, James M.; Pessah, Martin E.
  • The Astrophysical Journal, Vol. 713, Issue 1
  • DOI: 10.1088/0004-637X/713/1/52

Magnetorotational dynamo chimeras: The missing link to turbulent accretion disk dynamo models?⋆
journal, February 2017


Large-Scale Azimuthal Structures of Turbulence in Accretion Disks: Dynamo Triggered Variability of Accretion
journal, December 2011


On hydrodynamic shear turbulence in Keplerian disks: Via transient growth to bypass transition
journal, April 2003


Bypass to Turbulence in Hydrodynamic Accretion Disks: An Eigenvalue Approach
journal, August 2005

  • Mukhopadhyay, Banibrata; Afshordi, Niayesh; Narayan, Ramesh
  • The Astrophysical Journal, Vol. 629, Issue 1
  • DOI: 10.1086/431419

Magnetized stratified rotating shear waves
journal, February 2012


Aspect ratio dependence in magnetorotational instability shearing box simulations
journal, June 2008


Nonlinear transverse cascade and two-dimensional magnetohydrodynamic subcritical turbulence in plane shear flows
journal, April 2014

  • Mamatsashvili, G. R.; Gogichaishvili, D. Z.; Chagelishvili, G. D.
  • Physical Review E, Vol. 89, Issue 4
  • DOI: 10.1103/PhysRevE.89.043101

Transient growth of perturbations on scales beyond the accretion disc thickness
journal, February 2017

  • Razdoburdin, D. N.; Zhuravlev, V. V.
  • Monthly Notices of the Royal Astronomical Society, Vol. 467, Issue 1
  • DOI: 10.1093/mnras/stx050

Regimes of the non-exponential temporal growth in thin Keplerian discs under toroidally dominated magnetic fields: Keplerian discs in toroidal magnetic fields
journal, January 2012


Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow
journal, February 2015


The onset of shear flow turbulence
journal, April 2000


Magnetic flux Concentration and Zonal Flows in Magnetorotational Instability Turbulence
journal, November 2014


Universal small-scale structure in turbulence driven by magnetorotational instability
journal, February 2017

  • Zhdankin, Vladimir; Walker, Justin; Boldyrev, Stanislav
  • Monthly Notices of the Royal Astronomical Society, Vol. 467, Issue 3
  • DOI: 10.1093/mnras/stx372

Energy transfer in anisotropic magnetohydrodynamic turbulence
journal, April 2009


On the angular momentum transport due to vertical convection in accretion discs
journal, May 2010


Symmetries, Scaling Laws, and Convergence in Shearing-Box Simulations of Magneto-Rotational Instability Driven Turbulence
journal, September 2011


MRI channel flows and their parasites
journal, April 2009

  • Latter, Henrik N.; Lesaffre, Pierre; Balbus, Steven A.
  • Monthly Notices of the Royal Astronomical Society, Vol. 394, Issue 2
  • DOI: 10.1111/j.1365-2966.2009.14395.x

Saturation of the magnetorotational instability in the unstratified shearing box with zero net flux: convergence in taller boxes
journal, December 2015

  • Shi, Ji-Ming; Stone, James M.; Huang, Chelsea X.
  • Monthly Notices of the Royal Astronomical Society, Vol. 456, Issue 3
  • DOI: 10.1093/mnras/stv2815

Hydrodynamic Stability Without Eigenvalues
journal, July 1993


The nuclear stellar disc in Andromeda: a fossil from the era of black hole growth: Origin of the eccentric disc and BH in M31
journal, April 2010


Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics
journal, August 2007


A Powerful Local Shear Instability in Weakly Magnetized Disks. IV. Nonaxisymmetric Perturbations
journal, November 1992

  • Balbus, Steven A.; Hawley, John F.
  • The Astrophysical Journal, Vol. 400
  • DOI: 10.1086/172022

Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept
journal, August 2016


Statistical theory of magnetohydrodynamic turbulence: recent results
journal, November 2004


Parasitic instabilities in magnetized, differentially rotating disks
journal, September 1994

  • Goodman, Jeremy; Xu, Guohong
  • The Astrophysical Journal, Vol. 432
  • DOI: 10.1086/174562

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows
journal, September 2011


Angular Momentum Transport in Accretion Disks: Scaling Laws in MRI-driven Turbulence
journal, September 2007

  • Pessah, Martin E.; Chan, Chi-kwan; Psaltis, Dimitrios
  • The Astrophysical Journal, Vol. 668, Issue 1
  • DOI: 10.1086/522585

On characterizing non-locality and anisotropy for the magnetorotational instability
journal, May 2014

  • Nauman, F.; Blackman, E. G.
  • Monthly Notices of the Royal Astronomical Society, Vol. 441, Issue 3
  • DOI: 10.1093/mnras/stu706

Turbulence and Steady Flows in Three-Dimensional Global Stratified Magnetohydrodynamic Simulations of Accretion Disks
journal, June 2011


On the stability of an accretion disc containing a toroidal magnetic field
journal, April 1996

  • Terquem, C.; Papaloizou, J. C. B.
  • Monthly Notices of the Royal Astronomical Society, Vol. 279, Issue 3
  • DOI: 10.1093/mnras/279.3.767

Subcritical transition in channel flows
journal, January 2002


On Hydromagnetic Stresses in Accretion disk Boundary Layers
journal, May 2012


MHD simulations of the magnetorotational instability in a shearing box with zero net flux: I. The issue of convergence
journal, October 2007


MHD simulations of the magnetorotational instability in a shearing box with zero net flux: II. The effect of transport coefficients
journal, October 2007


On the nature of magnetic turbulence in rotating, shearing flows
journal, January 2016

  • Walker, Justin; Lesur, Geoffroy; Boldyrev, Stanislav
  • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 457, Issue 1
  • DOI: 10.1093/mnrasl/slv200

Angular redistribution of nonlinear perturbations: A universal feature of nonuniform flows
journal, June 2010


Magnetorotational Turbulence in Stratified Shearing Boxes with Perfect gas Equation of State and Finite Thermal Diffusivity
journal, December 2012


Impact of dimensionless numbers on the efficiency of magnetorotational instability induced turbulent transport
journal, June 2007


Convection Causes Enhanced Magnetic Turbulence in Accretion Disks in Outburst
journal, April 2014

  • Hirose, Shigenobu; Blaes, Omer; Krolik, Julian H.
  • The Astrophysical Journal, Vol. 787, Issue 1
  • DOI: 10.1088/0004-637X/787/1/1

MRI-driven turbulent transport: the role of dissipation, channel modes and their parasites
journal, June 2010


Global MHD simulations of stratified and turbulent protoplanetary discs: I. Model properties
journal, September 2006


Simulations of Magnetorotational Turbulence with a Higher-Order Godunov Scheme
journal, December 2008


Nonaxisymmetric stability in the shearing sheet approximation
journal, April 2006


Global simulations of magnetorotational turbulence – I. Convergence and the quasi-steady state
journal, August 2013

  • Parkin, E. R.; Bicknell, G. V.
  • Monthly Notices of the Royal Astronomical Society, Vol. 435, Issue 3
  • DOI: 10.1093/mnras/stt1450

Nonmodal Stability Theory
journal, January 2007


Non-linear energy transfers in accretion discs MRI turbulence: I. Net vertical field case
journal, February 2011


Zonal Flows and Long-Lived Axisymmetric Pressure Bumps in Magnetorotational Turbulence
journal, May 2009


Magnetorotational Instability: Nonmodal Growth and the Relationship of Global Modes to the Shearing box
journal, November 2014


On the Saturation of the Magnetorotational Instability via Parasitic Modes
journal, May 2009


Global Simulations of Accretion Disks. i. Convergence and Comparisons with Local Models
journal, April 2012

  • Sorathia, Kareem A.; Reynolds, Christopher S.; Stone, James M.
  • The Astrophysical Journal, Vol. 749, Issue 2
  • DOI: 10.1088/0004-637X/749/2/189