Progress report on a digital experiment in spiral turbulence.

Abstract

The following nine papers were pre,.;cntc<.l at the AIAA ..-\erothermochemistry of Turbulent F lows Conference in Sa n Diego, Calif., December 13-15, 1965. The Organizing Committee of the conference con:-:istecl of H. Yoshihara, Chairman, R. vanclen B erg, . C. Lin, W. X achbar, T . Y. Tong, and F. A . William;;. The re,·ie,,· procedure for these paper,.; w a..; ha ndled by P aul A. Libb~·. Progress Report on a Digital Experiment in Spiral TurbulenceDoxALD CoLEti* A~D CHARLES VA~ ATTA t Calijomia I nslilute of T echnology, Pasadena, Calif.Dig ital hot-wi1·e l echn i<Jues h ave bee n u sed to measure the tangentia l 'aria lion of th e vector m e an veloci ty and the ,..;x Heynold s ;;t,·e,.,.es at one radial pos ition in a statistica ll y s tationary •nixe d laminat·-turhule nt flow betwe en counte rrotating con cen tric cylindet·s. 1.:\TER~IITI E.:\T spiral flow patterns like the one shown in F ig. I are known to be typical of transition in circular Couette flow when the two cylinders rotate in oppo::ite direction . -4The spiral band of turbulence rotates steadily at \·ery nearly the mean speed of the two cylinder:<. so that a given element of flu id near either wall must participate alternately in the laminar and turbulent motions. A question therefore ari~es as to energy proce ses that occur near the in terfaces ~eparating laminar and turbulent regions of flow.In 1958, a research program was begun at Graduate Aeronautical Laboratories California In t itute of Technology 1GALCIT) to tudy this question experimentally in a large !'}'Iinder apparatus using air a a working fluid and hot wires as primary in trumentation . The technique involves repeated sampl ing of signals from a calibrated multiple hotwire array so as to obtain an ensemble of values for the instantaneou ,·ector velocity at a large number of points fixed in the rotating pattern. The research has therefore required the breaking of new groUlld in the application of high-speed ,ampling and computing equipment to experimental work in turbulence.The particular flow chosen for detailed study 3 ·' i~ at quite low Reynolds number (Ro = 50,000 , R , = -5,600 based on radius and surface velocity), with air velocities relati,·e to a probe moUllted on one or t he other cylinders of about 3 to 5 fps. The spiral pattern is left-handed and makes an angle of about 62° wi th the cylinder axis of rotation.In the fa ll of 1962, analog tape recordings were made of "ignals from a hot-wire array in this flow. About 3500 cycles of the flow pattern were recorded at each of 17 radial po itions across the annulus. These analog data have been used directly 3 · ' to determine the mean shape of t he turbulent re~ion, with the result h01m in Fig. 2.In 1963, electronic data-processing equipment at the Jet Propulsion Laboratory was used to obtain digital samples of the hot~,,·ire \'Oltages at about 60 points in each laminarturbulent cycle of each analog tape (about 1 0 million binary bits of information in all). The resulting voltage data were processed once by computer 3 to corr...

From temporal to spatiotemporal dynamics in transitional plane Couette flow

“…During the last few years there has been a resurgence of interest regarding the formation of laminar-turbulent patterns in wall-bounded shear flows having very large aspect ratios (when the lateral dimensions, along x and z, are more than two orders of magnitude larger than the relevant wall-normal dimension, along y). The phenomenon was discovered in circular Couette flow (CCF) by Coles and Van Atta [8,9] who called it 'spiral turbulence'. The pattern can be observed when the two cylinders of CCF rotate in opposite directions in a specific velocity range, which is only a part of the complete bifurcation diagram [1].…”

Direct numerical simulation of spiral turbulence

“…The co-existence of two distinct dynamical states at the same values of the control parameters has also been found in other kinds of dynamical systems; see Cross & Hohenberg (1993) and Berge, Pomeau & Vidal (1984) for a review of related aspects. Coles (1965) 0.874, 0.889 13.95, 15 0-15 000 −10 000 to −80 000 Van Atta (1966) 0.889 8.5-13.75 −10 000 to 20 000 −10 000 to −170 000 Coles & Van Atta (1966) 0.889 ? −5600 50 000 Coles & Van Atta (1967) 0.889 ?…”

Turbulent-Laminar Patterns in Plane Couette Flow

“…We have verified the accuracy of our simulations in small domains by comparing to prior simulations [10]. In large domains we have examined mean velocities, Reynolds stresses, and correlations in a turbulent-laminar flow at Re = 350 and find that these reproduce experimental results from Taylor-Couette [5] and plane Couette [11] flow. While neither experimental study corresponds exactly to our case, the agreement supports our claim that our simulations correctly capture turbulent-laminar states.…”

“…In the mid 1960s a state known as spiral turbulence was first discovered [4,5,26] in counter-rotating Taylor-Couette flow. This state consists of a turbulent and a laminar region, each with a spiral shape.…”