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Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Mukhopadhyay, Banibrata and Mathew, Ranchu and Raha, Soumyendu (2011) Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows. In: New Journal of Physics, 13 .

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Official URL: http://iopscience.iop.org/1367-2630/13/2/023029/


Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Item Type: Journal Article
Publication: New Journal of Physics
Publisher: IOP Publishing ltd
Additional Information: Copyright of this article belongs to IOP Publishing ltd.
Department/Centre: Division of Interdisciplinary Sciences > Supercomputer Education & Research Centre
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 24 Mar 2011 06:05
Last Modified: 24 Mar 2011 06:05
URI: http://eprints.iisc.ac.in/id/eprint/36181

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