Precision Measurements of Stretching and Compression in Fluid Mixing Greg A. Voth, George Haller, and Jerry Gollub

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## Animations (AVI format)

(Currently this is 37 Mb--I am working on a smaller one.) Animation showing the development of the persistent pattern in dye mixing experiments. On the left is a movie of the time dependent concentration field, while the right is only updated once per period. Note the approach to a constant pattern on the right, and the unmixed islands.
(3.6 Mb) Animation showing the position and velocity magnitude of all measured particles. All particles at the same phase of the forcing are shown together, and the animation evolves through one period of the forcing. Amid the generally random placement of the particles, note the elliptical structures that reveal a particle trapped in an island.
(1.7 Mb) Evolution of the lines of the compression field as the time delay used in the flow map (Delta t) is varied from 0.1 periods to 5 periods. p=1, Re=45.
(0.7 MB) One period of the evolution of the lines of the compression field overlayed on the corresponding dye images. Note how the compression lines align with the contour lines of the dye images. p=1, Re=45. Delta t = 3 periods.
(1.7 Mb) Animation of the time dependence of both the compression and stretching lines. These correspond to the stable and unstable manifolds of the flow. Crossings of the two manifolds that return to their original position after one period are hyperbolic fixed points. Observe how the "lobes" outlined by the manifolds are stretched as they approach the fixed points. p=1, Re=45. Delta t = 3 periods.
(6.6 Mb) Same as above, except now at p=5, Re=100. The fixed points are much more difficult to identify, although several of them can be found if the animation is studied carefully.
(3.5 Mb) This shows the time dependence of the compression lines and the dye in the flow at p=5, Re=100. The flow now appears as a random vortex flow, but the compression lines still align the dye pattern.

July 12, 2001
gvoth@haverford.edu