Low dimensional chaos in a hydrodynamic system
Abstract
Improved LDV techniques are used to study the onset of turbulence in the CouetteTaylor system. Dynamical system theory is first introduced and related to turbulence in hydrodynamic systems. The experimental techniques are described, including laser Doppler velocimetry, photon correlation, data acquisition, and mechanics. Phase space portraits, Poincare sections, calculations of the largest Lyapunov exponent, and the fractal dimension show that weakly turbulent motion in the CouetteTaylor system can be described by a lowdimensional strange attractor evolving out of a twotorus. At the critical point for the onset of chaos the largest Lyapunov exponent becomes positive and the attractor dimension increases from 2.0 to 2.5. At higher Reynolds numbers the number of positive Lyapunov exponents increases and the attractor dimension increases to about 3.2.
 Publication:

Ph.D. Thesis
 Pub Date:
 1984
 Bibcode:
 1984PhDT........16F
 Keywords:

 Chaos;
 Flow Theory;
 Hydrodynamic Equations;
 Strange Attractors;
 Transition Flow;
 Turbulent Flow;
 Couette Flow;
 Critical Point;
 Flow Measurement;
 Flow Visualization;
 Fractals;
 Laser Doppler Velocimeters;
 Liapunov Functions;
 Fluid Mechanics and Heat Transfer