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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2851

Title: Hydrodynamic fluctuations in the Kolmogorov flow: Nonlinear regime
Authors: BENA, Ioana
Baras, F.
Mansour, M.M.
Issue Date: 2000
Publisher: AMERICAN PHYSICAL SOC
Citation: PHYSICAL REVIEW E, 62(5). p. 6560-6570
Abstract: In a previous paper [I. Bena, RI. Malek Mansour, and F. Baras, Phys. Rev. E 59, 5503 (1999)] the statistical properties of Linearized Iiolmogorov flow were studied, using the formalism of fluctuating hydrodynamics. In this paper the nonlinear regime is considered, with emphasis on the statistical properties of the flow near the first instability. The normal form amplitude equation is derived for the case of an incompressible fluid and the velocity field is constructed explicitly above (but close to) the instability. The relative simplicity of this flow allows one to analyze the compressible case as well. Using a perturbative technique, it is shown that close to the instability threshold the stochastic dynamics of the system is governed by two coupled nonlinear Langevin equations in Fourier space. The solution of these equations can be cast into the exponential of a Landau-Ginzburg functional, which proves to be identical to the one obtained for the case of an incompressible fluid. The theoretical predictions are confirmed by numerical simulations of the nonlinear fluctuating hydrodynamic equations.
Notes: Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium. Free Univ Brussels, Ctr Nonlinear Phenomena & Complex Syst, B-1050 Brussels, Belgium.Bena, I, Limburgs Univ Ctr, Univ Campus, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/2851
DOI: 10.1103/PhysRevE.62.6560
ISI #: 000165341700090
ISSN: 1063-651X
Category: A1
Type: Journal Contribution
Validation: ecoom, 2001
Appears in Collections: Research publications

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