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Structural stability theory of two-dimensional fluid flow under stochastic forcing

Published online by Cambridge University Press:  15 July 2011

NIKOLAOS A. BAKAS  and
PETROS J. IOANNOU
NIKOLAOS A. BAKAS*
Affiliation:
Department of Physics, National and Kapodistrian University of Athens, Office 32, Building IV, Panepistimiopolis, 15784 Athens, Greece
PETROS J. IOANNOU
Affiliation:
Department of Physics, National and Kapodistrian University of Athens, Office 32, Building IV, Panepistimiopolis, 15784 Athens, Greece
*
†Email address for correspondence: [email protected]
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Abstract

Large-scale mean flows often emerge in turbulent fluids. In this work, we formulate a stability theory, the stochastic structural stability theory (SSST), for the emergence of jets under external random excitation. We analytically investigate the structural stability of a two-dimensional homogeneous fluid enclosed in a channel and subjected to homogeneous random forcing. We show that two generic competing mechanisms control the instability that gives rise to the emergence of an infinitesimal jet: advection of the eddy vorticity by the mean flow that is shown to be jet forming and advection of the vorticity gradient of the jet by the eddies that is shown to hinder the formation of the mean flow. We show that stochastic forcing with small streamwise coherence and an amplitude larger than a certain threshold leads to the emergence of jets in the channel through a bifurcation of the non-linear SSST system.

JFM classification

Mathematical Foundations: General fluid mechanics Instability: Instability Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 332 - 361
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

‡

Present address: National and Kapodistrian University of Athens, Build. IV office 32, Panepistimiopolis, Zografos, Athens, Greece.

References

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