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Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation

Ghosh, S and Mukhopadhyay, B (2020) Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation. In: Monthly Notices of the Royal Astronomical Society, 496 (4). pp. 4191-4208.

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Official URL: https:dx.doi.org/10.1093/mnras/staa1780


Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long-standing puzzle. These flows are linearly stable. Here we explore the evolution of perturbation in such flows in the presence of an additional force. Such a force, which is expected to be stochastic in nature hence behaving as noise, could be result of thermal fluctuations (however small be), Brownian ratchet, grain-fluid interactions, feedback from outflows in astrophysical discs, etc. We essentially establish the evolution of nonlinear perturbation in the presence of Coriolis and external forces, which is modified Landau equation. We show that even in the linear regime, under suitable forcing and Reynolds number, the otherwise least stable perturbation evolves to a very large saturated amplitude, leading to nonlinearity and plausible turbulence. Hence, forcing essentially leads a linear stable mode to unstable. We further show that nonlinear perturbation diverges at a shorter time-scale in the presence of force, leading to a fast transition to turbulence. Interestingly, emergence of nonlinearity depends only on the force but not on the initial amplitude of perturbation, unlike original Landau equation based solution. © 2020 The Author(s).

Item Type: Journal Article
Publication: Monthly Notices of the Royal Astronomical Society
Publisher: Oxford University Press
Additional Information: The copyright of this article belongs to Oxford University Press
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 24 Feb 2021 11:22
Last Modified: 24 Feb 2021 11:22
URI: http://eprints.iisc.ac.in/id/eprint/67400

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