Passive advection of fractional Brownian motion by random layered flows
Résumé
We study statistical properties of the process Y(t) of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion X(t) with the Hurst index H ä (0,1). We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time t limit in proportion tot H 2 , which defines a family of anomalous super-diffusions. We evaluate the disorder-averaged Wigner-Ville spectrum of the advection process Y(t) and demonstrate that it has a rather unusual power-law form-f 1 H 3 with a characteristic exponent which exceed the value 2. Our results also suggest that sample-to-sample fluctuations of the spectrum can be very important.
Domaines
Physique [physics]Origine | Publication financée par une institution |
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