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Hydrodynamic Fluctuations in Laminar Fluid Flow. I. Fluctuating Orr-Sommerfeld Equation

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Abstract

In recent years it has become evident that fluctuating hydrodynamics predicts that fluctuations in nonequilibrium states are always spatially long ranged. In this paper we consider the application of fluctuating hydrodynamics to laminar fluid flow, using plane Couette flow as a representative example. Specifically, fluctuating hydrodynamics yields a stochastic Orr-Sommerfeld equation for the wall-normal velocity fluctuations, where spontaneous thermal noise acts as a random source.This stochastic equation needs to be solved subject to appropriate boundary conditions. We show how an exact solution can be obtained from an expansion in terms of the eigenfunctions of the Orr-Sommerfeld hydrodynamic operator. We demonstrate the presence of a flow-induced enhancement of the wall-normal velocity fluctuations and a resulting flow-induced energy amplification and provide a quantitative analysis how these quantities depend on wave number and Reynolds number.

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Authors and Affiliations

  1. Departamento de Física Aplicada I, Facultad de Física, Universidad Complutense, 28040, Madrid, Spain

    J. M. Ortiz de Zárate

  2. Institute for Physical Science and Technology and Burgers Program for Fluid Dynamics, University of Maryland, College Park, MD, 20740-8510, USA

    J. V. Sengers

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  1. J. M. Ortiz de Zárate
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  2. J. V. Sengers
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Correspondence to J. M. Ortiz de Zárate.

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Ortiz de Zárate, J.M., Sengers, J.V. Hydrodynamic Fluctuations in Laminar Fluid Flow. I. Fluctuating Orr-Sommerfeld Equation. J Stat Phys 144, 774–792 (2011). https://doi.org/10.1007/s10955-011-0256-1

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  • DOI: https://doi.org/10.1007/s10955-011-0256-1

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