Fractional Brownian Motion Limit for a Model of Turbulent Transport
Albert Fannjiang (UC Davis), Tomasz Komorowski (Maria, Curie-Sk{\l}odowska University)
TL;DR
This paper demonstrates that passive scalar motion in certain Gaussian velocity fields with long-range correlations converges to fractional Brownian motion over long times, revealing new insights into turbulent transport modeling.
Contribution
It establishes a fractional Brownian motion limit for passive scalar transport in Gaussian velocity fields with long-range correlations, a novel theoretical result.
Findings
Passive scalar motion converges to fractional Brownian motion.
Long-range correlations in velocity fields influence scalar transport.
The model provides a new framework for understanding turbulent diffusion.
Abstract
Passive scalar motion in a family of random Gaussian velocity fields with long-range correlations is shown to converge to persistent fractional Brownian motions in long times.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Stochastic processes and statistical mechanics