Dependence of Two-Dimensional Chaotic Mixing on Reynolds Number
Abstract
We have extended a previous study footnote D. Rothstein, E. Henry, and J.P. Gollub, Nature, 401, 770 (1999). of two-dimensional chaotic mixing in a stratified fluid carrying a time-periodic current in the presence of an array of magnets. Two important control parameters have been identified: the Reynolds number Re, and a forcing parameter p that gives the dimensionless mean path length of a fluid element in one half period of forcing. We study the mixing process by monitoring the intensity field I(x,y) of a fluorescent dye initially confined to one half of the fluid layer. We have studied the mixing rate m, defined as the global exponential decay rate of the standard deviation I(x,y), as a function of these parameters. We note several surprising results. First, m is a non-monotonic function of p, apparently as a result of geometrical resonances between the typical path length and the spatial structure of the forcing. Second, m apparently reaches a maximum as a function of Re, declining at high Re. We present a dynamical systems argument as to why such a decline might occur.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 2000
- Bibcode:
- 2000APS..DFD.JB005D