Laser Doppler Velocimetry Study of the Onset of Chaos in Taylor Vortex Flow.

The Laser Doppler Velocimetry technique was used to study the mechanism by which chaos can appear in a system governed by deterministic equations of motion and time -independent boundary conditions. Incompressible fluid flow between concentric cylinders, induced by the rotation of the inner one with the outer one fixed, was chosen because it displays a progression of instabilties with increasing Reynolds number before the onset of chaos. Early workers {1} thought the number of instabilities so large that the flow appears chaotic when it is actually highly multiply-periodic. Recent work {2} cast doubt on this picture. The present study used a mini-computer on line to a PDP-10 mainframe to acquire long data records. The computed velocity power spectral densities therefore had a resolution of (10('-4)). High optical mixing efficiency provided a signal to noise ratio three orders of magnitude higher than previous studies. As a result, we have been able to precisely characterize a quasi-periodic flow and show that chaos appears after two time-dependent instabilities. Relationships of the mode frequencies at the onset of chaos are examined. ('1)Landau, L. 1944 "On the problem of turbulence." C. R. (Dokl.) Acad. Sci. URSS 44, 311-315. ('2)Gollub, J. P. and Swinney, H. L. 1975 "Onset of turbulence in a rotating fluid." Phys. Rev. Lett. 35, 927-930.