Greg Voth, Haverford College
George Haller, Brown Unversity
Jerry Gollub, Haverford College and Univ. of Pennsylvania
Using precision measurements of tracer particle trajectories in a two-dimensional
fluid flow producing
chaotic mixing, we directly measure the time-dependent stretching field.
This quantity, which was
previously available only numerically, attains local maxima along lines
that coincide with the stable and
unstable manifolds of hyperbolic fixed points of Poincare maps. Dye
concentration fields are measured
in the same flow as the stretching fields, and we demonstrate the way
that lines of fluid points that have
recently experienced large stretching coincide with contours of the
dye concentration. We also explore the
probability distribution of stretching and applications to the prediction
of mixing rates.