Largedeviation joint statistics of the finitetime Lyapunov spectrum in isotropic turbulence
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finitetime Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the socalled Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finitesize correction to the histogrambased method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEsmore »
 Authors:

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 Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218 (United States)
 Publication Date:
 OSTI Identifier:
 22482475
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DATASETS; DEFORMATION; DROPLETS; EIGENVALUES; FLUIDS; LAGRANGIAN FUNCTION; LYAPUNOV METHOD; STATISTICAL MODELS; STATISTICS; SYMMETRY; TURBULENCE; TURBULENT FLOW; VELOCITY