Fluctuation relation and pairing rule for Lyapunov exponents of inertial particles in turbulence - Nonlinear Sciences > Chaotic DynamicsReport as inadecuate




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Abstract: We study the motion of small particles in a random turbulent flow assuminglinear law of friction. We derive a symmetry relation obeyed by the largedeviations of the finite time Lyapunov exponents in the phase space. Therelation applies when either the statistics of the strain matrix is invariantunder the transposition or when it is time-reversible. We show that, as aresult, the Lyapunov exponents come in pairs which sum is equal to minus theinverse relaxation time of the particles. We use the pairing to consider theKaplan-Yorke dimension of the particles attractor in the phase space. Inparticular, the results apply to case of the flow which is white noise in time.



Author: Itzhak Fouxon, Péter Horvai

Source: https://arxiv.org/



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