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Fractal tracer distributions in turbulent field theories

Jonas Lundbek Hansen·Tomas Bohr
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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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Jonas Lundbek Hansen, Tomas Bohr. 1997-09-09. Fractal tracer distributions in turbulent field theories. https://arxiv.org/abs/chao-dyn/9709008

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