Fractal tracer distributions in turbulent field theories

1997/09/09 by Jonas Lundbek Hansen, Tomas Bohr, Hansen, Jonas Lundbek +1
Economics, Econometrics and Finance · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Quantum chaos and dynamical systems #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.chao-dyn/9709008

openalex publication_date 1997/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and thereby find a regime in which the particle distribution is a strange attractor. We compare the Lyapunov dimension to the information dimension of actual particle distributions and show that there is good agreement with the Kaplan-Yorke conjecture. Similar phenomena have been observed experimentally.

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