### Abstract

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise. © 2013 American Physical Society.

Original language | English |
---|---|

Article number | 013010 |

Journal | Physical Review E |

Volume | 88 |

Issue number | 1 |

DOIs | |

Publication status | Published - 17 Jul 2013 |

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### Keywords

- cross-correlations
- magneto-hydrodynamic flow
- magnetohydrodynamic stability
- magnetorotational instability
- radial coordinates
- rotating shear flow
- temporal and spatial
- weak magnetic fields
- angular velocity
- astrophysics
- autocorrelation
- energy dissipation
- magnetohydrodynamics
- stochastic systems
- shear flow

### Cite this

*Physical Review E*,

*88*(1), [013010]. https://doi.org/10.1103/PhysRevE.88.013010

}

*Physical Review E*, vol. 88, no. 1, 013010. https://doi.org/10.1103/PhysRevE.88.013010

**Magnetohydrodynamic stability of stochastically driven accretion flows.** / Nath, Sujit K.; Mukhopadhyay, Banibrata; Chattopadhyay, Amit K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Magnetohydrodynamic stability of stochastically driven accretion flows

AU - Nath, Sujit K.

AU - Mukhopadhyay, Banibrata

AU - Chattopadhyay, Amit K.

PY - 2013/7/17

Y1 - 2013/7/17

N2 - We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise. © 2013 American Physical Society.

AB - We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise. © 2013 American Physical Society.

KW - cross-correlations

KW - magneto-hydrodynamic flow

KW - magnetohydrodynamic stability

KW - magnetorotational instability

KW - radial coordinates

KW - rotating shear flow

KW - temporal and spatial

KW - weak magnetic fields

KW - angular velocity

KW - astrophysics

KW - autocorrelation

KW - energy dissipation

KW - magnetohydrodynamics

KW - stochastic systems

KW - shear flow

UR - http://www.scopus.com/inward/record.url?scp=84880582147&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.88.013010

DO - 10.1103/PhysRevE.88.013010

M3 - Article

VL - 88

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 013010

ER -