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Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

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Ortiz de Zárate Leira, José María and Sengers, Jan V. (2013) Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation. Journal of statistical physics, 150 (3). pp. 540-558. ISSN 0022-4715

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Official URL: http://dx.doi.org/10.1007/s10955-012-0495-9


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Abstract

We use fluctuating hydrodynamics to evaluate the enhancement of thermally excited fluctuations in laminar fluid flow using plane Couette flow as a representative example. In a previous publication (J. Stat. Phys. 144:774, 2011) we derived the energy amplification arising from thermally excited wall-normal fluctuations by solving a fluctuating Orr-Sommerfeld equation. In the present paper we derive the energy amplification arising from wall-normal vorticity fluctuation by solving a fluctuating Squire equation. The thermally excited wall-normal vorticity fluctuations turn out to yield the dominant contribution to the energy amplification. In addition, we show that thermally excited streaks, even in the absence of any externally imposed perturbations, are present in laminar fluid flow.


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© Springer Science+Business Media, LLC 2012.
The authors acknowledge stimulating discussions with Andreas Acrivos, Bruno Eckhardt and Mihailo Jovanovic. The research was supported by the Spanish Ministry of Science and Innovation through research grant FIS2008-03801.

Uncontrolled Keywords:Energy amplification; Fluctuating hydrodynamics; Laminar fluid flow; Orr-Sommerfeld equation; Plane Couette flow; Squire equation; Vorticity fluctuations
Subjects:Sciences > Physics
ID Code:35317
Deposited On:27 Jan 2016 16:39
Last Modified:27 Jan 2016 16:39

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