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 <R> is larger than the integral scale, the distribution of shapes is Gaussian. When the size of the triangle <R> 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)].
Castiglione
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Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France.
Pumir
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