Measurements of stretching fields in chaotic mixing experiments

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.