Stochastically driven instability in rotating shear flows

Banibrata Mukhopadhyay, Amit Chattopadhyay

Research output: Contribution to journalArticle

Abstract

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is on flows whose angular velocities decrease but specific angular momenta increase with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We focus on a small section of such a flow which is essentially a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations, that presumably generate instability. A range of angular velocity profiles (for the steady flow), starting with the constant angular momentum to that of the constant circular velocity are explored. It is shown that the growth and roughness exponents calculated from the contour (envelope) of the perturbed flows are all identical, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive stochastic noise to the underlying linearized governing equations. This has important implications in resolving the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

Original languageEnglish
Article number035501
Number of pages17
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number3
Early online date21 Dec 2012
DOIs
Publication statusPublished - 25 Jan 2013

Fingerprint

Rotating Flow
Shear flow
Shear Flow
shear flow
Turbulence
Hydrodynamics
Angular momentum
Angular velocity
turbulence
hydrodynamics
Accretion Disks
angular velocity
accretion disks
magnetohydrodynamics
Angular Momentum
astrophysics
Rayleigh
Steady flow
angular momentum
Magnetohydrodynamics

Bibliographical note

Creative Commons Attribution 3.0 Unported

Keywords

  • hydrodynamics
  • instabilities
  • turbulence
  • statistical mechanics
  • accretion disks

Cite this

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Stochastically driven instability in rotating shear flows. / Mukhopadhyay, Banibrata; Chattopadhyay, Amit.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 3, 035501, 25.01.2013.

Research output: Contribution to journalArticle

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