Pattern Fluctuations in Transitional Plane Couette Flow
Abstract
In wide enough systems, plane Couette flow, the flow established between two parallel plates translating in opposite directions, displays alternatively turbulent and laminar oblique bands in a given range of Reynolds numbers R. We show that in periodic domains that contain a few bands, for given values of R and size, the orientation and the wavelength of this pattern can fluctuate in time. A procedure is defined to detect welloriented episodes and to determine the statistics of their lifetimes. The latter turn out to be distributed according to exponentially decreasing laws. This statistics is interpreted in terms of an activated process described by a Langevin equation whose deterministic part is a standard Landau model for two interacting complex amplitudes whereas the noise arises from the turbulent background.
 Publication:

Journal of Statistical Physics
 Pub Date:
 February 2011
 DOI:
 10.1007/s109550110126x
 arXiv:
 arXiv:1101.2513
 Bibcode:
 2011JSP...142..577R
 Keywords:

 Fluid dynamics;
 Turbulence;
 Pattern formation;
 Jump process;
 Physics  Fluid Dynamics;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 13 pages, 11 figures. Accepted for publication in Journal of statistical physics