Bandi, Mahesh M
(2006)
An Experimental Investigation of Nonequilibrium Physics and Dynamical Systems in Turbulent Fluids.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Experiment 1 studies finite system size effects on temporal energy flux fluctuations in threedimensional (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 thirdorder 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 secondorder Lagrangian structure function should scale linearly in time. However the experimental measurements show it instead scales as a powerlaw with exponent 1/2. Experiment 3 concerns measurement of entropy production rate in steadystate 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 SteadyState 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.
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Details
Item Type: 
University of Pittsburgh ETD

Status: 
Unpublished 
Creators/Authors: 

ETD Committee: 

Date: 
6 October 2006 
Date Type: 
Completion 
Defense Date: 
14 July 2006 
Approval Date: 
6 October 2006 
Submission Date: 
10 August 2006 
Access Restriction: 
No restriction; Release the ETD for access worldwide immediately. 
Institution: 
University of Pittsburgh 
Schools and Programs: 
Dietrich School of Arts and Sciences > Physics 
Degree: 
PhD  Doctor of Philosophy 
Thesis Type: 
Doctoral Dissertation 
Refereed: 
Yes 
Uncontrolled Keywords: 
Dynamical Systems; Fluid Turbulence; Nonequilibrium Physics; Nonlinear Dynamics; Statistical Mechanics 
Other ID: 
http://etd.library.pitt.edu/ETD/available/etd08102006020453/, etd08102006020453 
Date Deposited: 
10 Nov 2011 19:58 
Last Modified: 
15 Nov 2016 13:48 
URI: 
http://dscholarship.pitt.edu/id/eprint/9034 
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