Spiral turbulence in circular Couette flow

• Main Author: Van Atta, Charles W.
• Format: Others
• Published: 1965
• Online Access: https://thesis.library.caltech.edu/347/1/Van_Atta_cw_1965.pdf; Van Atta, Charles W. (1965) Spiral turbulence in circular Couette flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/73GQ-A629. https://resolver.caltech.edu/CaltechETD:etd-01262004-102054 <https://resolver.caltech.edu/CaltechETD:etd-01262004-102054>

Under certain conditions, the fluid motion between counter-rotating concentric cylinders is made up of alternate helical stripes of laminar and turbulent flow. The present experiments show that, over a large range of cylinder Reynolds numbers, this helical pattern of turbulence rotates steadily at very nearly the mean angular velocity of the two cylinders. When the speed of the outer cylinder is held fixed and the speed of the inner cylinder increases from rest in the opposite direction, spiral turbulence follows a catastrophic breakdown of the toroidal vortices arising from Taylor instability. The ultimate objective of the present experiments is to measure the local rate of energy transfer between the turbulence and the mean motion in a typical spiral turbulent flow. The working fluid is air, and the instrumentation consists of hot-wire anemometers together with a variety of devices for operating on the resulting signals. Each cycle of the mixed laminar-turbulent flow (as observed by a probe mounted on one or the other cylinder) is treated as a member of an ensemble of realizations. The energy transfer (in a coordinate system rotating with the mean velocity of the turbulence) can be determined by averaging over a large number of instantaneous velocity samples taken at corresponding points in successive cycles of the turbulence. After some exploratory measurements, particular flow was selected for which the laminar-turbulent interfaces were sharply delineated across the entire annular gap and for which the dispersion in interface location was a minimum. This flow is about half laminar and half turbulent: it is characterized by a nose of turbulence associated with the leading interface and projecting into the laminar region near the outer cylinder, while a corresponding tail near the inner cylinder is associated with the trailing interface. The helical pattern is lefthanded and makes an angle of about 62 degrees with the axis of the cylinders. For the flow in question, analog voltage signals from a calibrated array of four hot wires were first recorded on magnetic tape. Several thousand cycles of turbulence were recorded at each of 17 different radial positions. Sampled values from these signals were then obtained and stored in digital form on magnetic tape, and were finally processed by a large electronic computer to restore the voltage data to the original laboratory units. The total amount of didital information available to describe the turbulence is roughly 180,000,000 bits. The amount of noise introduced into the individual sampled voltages by the recording, playback, digitizing, and processing operations so far carried out is believed to be no more than 3 parts in 10,000.