Stochastically driven instability in rotating shear flows

Abstract

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases 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 then the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic 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. 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 of perturbation, which presumably generate instability. A range of angular velocity (Ω) profiles of background flow, starting from that of constant specific angular momentum (λ= Ωr^2 ; r being the radial coordinate) to that of constant circular velocity (v_ϕ= Ωr), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of perturbations, 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 noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.

23 pages including 10 figures; to appear in Journal of Physics A: Mathematical and Theoretical

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Cited by in corpus (10)

• On the possible turbulence mechanism in accretion disks in non-magnetic binary stars
• Cross-correlation Aided Transport in Stochastically Driven Accretion Flows
• Magnetohydrodynamic stability of stochastically driven accretion flows
• A pure hydrodynamic instability in shear flows and its application to astrophysical accretion disks
• Double diffusivity model under stochastic forcing
• Origin of hydrodynamic instability from noise: from laboratory flow to accretion disk
• Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation
• Forced linear shear flows with rotation: rotating Couette-Poiseuille flow, its stability and astrophysical implications
• Noise-induced standing waves in oscillatory systems with time-delayed feedback
• The competition between the hydrodynamic instability from noise and magnetorotational instability in the Keplerian disks