An Experimental Investigation of Nonequilibrium Physics and Dynamical Systems in Turbulent Fluids.

摘要

Experiment 1 studies finite system size effects on temporal energy flux fluctuations in three-dimensional (3D) incompressible turbulence. The measured instantaneous energy flux shows that the turbulent energy transfer proceeds towards small spatial scales on average but frequently reverses direction (backscatter) to travel towards larger scales. The frequency of backscatter events is studied experimentally and through simulations. In Experiment 2 the third-order Eulerian structure function is measured for compressible turbulence on a free surface for the first time, and is found to scale linearly in space and agrees well with Kolmogorov's theory of 1941 (K41). K41 predicts the second-order Lagrangian structure function should scale linearly in time. However the experimental measurements show it instead scales as a power-law with exponent 1/2. Experiment 3 concerns measurement of entropy production rate in steady-state compressible turbulence. The analysis relies on the recent theory of Falkovich and Fouxon. The entropy rate is expected to equal the time integral of the lagrangian velocity divergence correlation function with a negative prefactor. The experimental results are found to disagree with this prediction. In addition, if the system is highly chaotic (follows SRB statistics), the system's entropy rate equals the sum of its Lyapunov exponents. The measured entropy rate agrees well with the sum of Lyapunov exponents obtained from simulations by Boffetta et. al. under flow conditions similar to the experiment. Experiment 4 presents a test of the Steady-State Fluctuation Theorem of Gallavotti and Cohen for entropy rate statistics collected from the individual lagrangian trajectories of experiment 3. The entropy rate statistics show excellent agreement with the Fluctuation Theorem within a limited interval of the probability distributions and limited window of averaging times.