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Relative dispersion in Lagrangian stochastic models
Leonid Piterbarg
University of Southern California
piter@math.usc.edu(Abstract received 04/14/2005 for session B)
ABSTRACT
A principal question for any multi particle LSM is whether it can reproduce observed regimes of the relative dispersion such as Richardson t-cubed and Batchelor exponential. We answer this question for two types of LSM, the Brownian flow (Kraichnan model) and a flow with memory (first order Markov model). For the Brownian flow exact scalings and their applicability limits are obtained. For the 'random flight' model both, local and non-local dynamics, are investigated. In the first case an exact exponential asymptotic is obtained for the relative dispersion. In turn, two regimes are considered in the case of non-smooth forcing: weak and strong turbulence. For weak turbulence the obtained asymptotic of relative dispersion is similar to that of the Brownian flow. As for strong turbulence, an upper bound is obtained for the scaling of relative dispersion.
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2005 LAPCOD Meeting, Lerici, Italy, June 13-17, 2005