Nonequilibrium velocity fluctuations and energy amplification in planar Couette flow

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In this paper we investigate intrinsic thermally excited nonequilibrium velocity fluctuations in laminar planar Couette flow. For this purpose we have complemented the solution of the stochastic Orr-Sommerfeld equation for the intensity of the fluctuations of the wall-normal velocity, presented in a previous publication, with a solution of the stochastic Squire equation for the intensity of the fluctuations of the wall-normal vorticity. We have obtained exact solutions of these equations without boundary conditions and solutions in a Galerkin approximation when appropriate boundary conditions are included. These results enable us to make a quantitative assessment of the intensity of these nonequilibrium fluctuations, as well as of the related energy amplification, which are always present, even in the absence of any externally imposed noise.
©2009 The American Physical Society. We are indebted to Frans T. M. Nieuwstadt, who called our attention to the problem addressed in this research. We are indebted to the Spanish Ministerio de Educacion y Ciencia for supporting J. V. S. during a sabbatical leave at the Universidad Complutense de Madrid where this work was initiated and for continued support through Research Project No. FIS2008-03801.
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