 Author
 Year
 2008
 Title
 Mixing and coherent structures in 2D viscous flows
 Journal
 Physica D
 Volume  Issue number
 237  1417
 Pages (fromto)
 19931997
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Institute for Theoretical Physics Amsterdam (ITFA)
 Abstract

We introduce a dynamical description based on a probability density phi(sigma, x, y, t) of the vorticity sigma in twodimensional viscous flows such that the average vorticity evolves according to the NavierStokes equations. A timedependent mixing index is defined and the class of probability densities that maximizes this index is studied. The time dependence of the Lagrange multipliers can be chosen in such a way that the masses m(sigma, t) := integral dxdy phi(sigma, x, y, t) associated with each vorticity value a are conserved. When the masses m(sigma, t) are conserved then (1) the mixing index satisfies an Htheorem and (2) the mixing index is the timedependent analogue of the entropy employed in the statistical mechanical theory of inviscid 2D flows. In the context of our class of probability densities we also discuss the reconstruction of the probability density of the quasistationary coherent structures from the experimentally determined vorticitystream function relations.
 URL
 go to publisher's site
 Language
 Undefined/Unknown
 Permalink
 http://hdl.handle.net/11245/1.299345
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