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Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic ChaosSeveral turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.
Document ID
19970001342
Acquisition Source
Legacy CDMS
Document Type
Technical Memorandum (TM)
Authors
Deissler, Robert G.
(NASA Lewis Research Center Cleveland, OH United States)
Date Acquired
September 6, 2013
Publication Date
September 1, 1996
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
NASA-TM-107028
E-9845
NAS 1.15:107028
Accession Number
97N11161
Funding Number(s)
PROJECT: RTOP 505-90-53
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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