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, previously available only numerically, attains local maxima along lines that coincide with the stable and unstable manifolds of hyperbolic fixed points of Poincaré maps. Contours of a passive impurity field are found at each instant to be oriented parallel to the lines that have recently experienced large stretching. The local stretching varies by 12 orders of magnitude.

• Received 30 November 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.254501