Finite size Lyapunov exponent for some simple models of turbulence |
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Authors: | Leonid I Piterbarg |
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Institution: | Department of Mathematics, University of Southern California, Kaprielian Hall, Room 108, 3620 Vermont Avenue, Los Angeles, CA 90089-2532, United States |
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Abstract: | Exact expressions for the finite size Lyapunov exponent λ(δ) are found and analyzed for several idealized models of turbulence in 1D and 2D. Among them are a random walk with discrete time and continuously distributed jumps and an isotropic Brownian flow in 2D also known as the Kraichnan flow. For the former a surprising fact is a δ−1 scaling for intermediate values of δ in contrast to δ−2 well known for a random walk in continuous time (Brownian flow) and for a simple random walk in discrete time. For the Kraichnan flow an exact relation is established between the scaling of λ(δ) and the scaling of relative dispersion in time. |
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Keywords: | Finite size Lyapunov exponent Random walk Kraichnan model |
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