Evolution of triangles in a two-dimensional turbulent flow.

As a turbulent flow advects a swarm of Lagrangian markers, the mutual separation between particles grows, and the shape of the swarm gets distorted. By following three points in an experimental turbulent two-dimensional flow with a k(-5/3) spectrum, we investigate the geometry of triangles, in a statistical sense. Two well-characterized shape distributions are identified. At long times when the average size of the triangles is larger than the integral scale, the distribution of shapes is Gaussian. When the size of the triangle is in the inertial range and grows as t(3/2) (Richardson's law), a plausibly self-similar, non-Gaussian probability distribution is observed, where very elongated triangles have a much larger probability than in the Gaussian regime. These results are discussed, and, in the latter case, compared with the predictions of a stochastic model recently introduced [A. Pumir et al., Phys. Rev. Lett. 85, 5324 (2000)].