Low dimensional chaos in a hydrodynamic system

Improved LDV techniques are used to study the onset of turbulence in the Couette-Taylor 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 Couette-Taylor system can be described by a low-dimensional strange attractor evolving out of a two-torus. 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.