On the Superdiffusive Behavior of Passive Tracer with a Gaussian Drift |
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Authors: | Tomasz Komorowski Stefano Olla |
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Institution: | (1) Institute of Mathematics, UMCS, pl. Marii Curie Sk odowskiej 1, 20-031 Lublin, Poland;(2) Département de Mathématiques, Université de Cergy Pontoise, 2 Av. Adolphe Chauvin, B.P. 222, 95302 Pontoise, Cergy-Pontoise-Cedex, France |
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Abstract: | In the present article we consider a motion of a passive tracer particle, whose trajectory satisfies the Itô stochastic differential equation d
x(t) = V(t, x(t)) dt +
d
w(t), where w(·) is a Brownian motion, V is a stationary Gaussian random field with incompressible realizations independent of w(·) and >0. We prove the superdiffusive character of the motion under certain conditions on the energy spectrum of the velocity field. The result is shown both for steady (time independent) and time dependent and Markovian velocity fields. In addition, we provide explicit upper and lower bounds for the Hurst exponent of the trajectory. All previous rigorous results concerned explicitely solvable shear flows cases. |
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Keywords: | passive tracer superdiffusion turbulent flow |
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