Large-Scale Finite-Wavelength Modulation within Turbulent Shear Flows

Abstract

Investigations of counter-rotating Taylor-Couette flow (TCF) in the narrow gap limit are conducted in a very large aspect ratio apparatus. The phase diagram is presented and compared to that obtained by Andereck et al. [1]. The spiral turbulence regime is studied by varying both internal and external Reynolds numbers. Spiral turbulence is shown to emerge from the fully turbulent regime via a continuous transition appearing first as a modulated turbulent state, which eventually relaxes locally to the laminar flow. The connection with the intermittent regimes of the plane Couette flow (pCf) is discussed. 47.20.Ft 47.20.Ky 47.54.+r, 47.27.Cn The "barber pole structure of turbulence" [2] between two counter-rotating cylinders, also called spiral turbulence, is commonly described as alternating helical stripes of laminar and turbulent flow. There are few quantitative studies of this puzzling regime, where long range order coexists with small scale turbulence. In early studies Coles and Van Atta [3][4][5] [6,7] described spiral turbulence within the framework of phase dynamics. All these studies were limited by their relatively small size. Only one helical turbulent stripe, winding no more than twice along the cylinder axis, could be observed. Altogether, the origin of this flow pattern remains unknown.Performing measurements in large aspect ratio TaylorCouette flow, we show that the spiral turbulence bifurcates continuously from the turbulent flow, appearing as a modulated turbulent state. After a rapid description of the experimental set up, we present the phase diagram and compare it to the one obtained by Andereck et al. [1] with a different cylinder radius ratio. Then we describe the successive steps leading to the fully turbulent flow before discussing the origin of spiral turbulence. Finally, we examine its breakdown into a spatio-temporal disordered regime similar to the laminar-turbulent coexistence dynamics observed in plane Couette flow [8,9]. We visualize the flow by a "fluorescent lighting "technique [10] developed for this study. The water flow is seeded with Kalliroscope AQ 1000 (6 × 30 × 0.07µm platelets). The inner cylinder is covered by a fluorescent film and the entire apparatus is UV-lighted. The fluorescent film re-emits a uniform visible lighting, transmitted through the fluid layer: the more turbulent the flow, the brighter it appears. As the gap is very thin, the Kalliroscope concentration is increased up to 25% by volume to enhance the contrast. A rheological study has shown that the fluid remains Newtonian, so that the only impact is a viscosity increase up to ν = 1.13 10 −6 m 2 /s at 20 • C. The flow is thermalized by water circulation inside the inner cylinder. At thermal equilibrium the temperature is uniform in space up to 0.1 • C and does not vary more than 0.1 • C/hour. Images and spatio-temporal diagrams (temporal recording of one line along the cylinder axis) are recorded by a CCD camera. Two plane mirrors reflect the two thirds of the flow hidden to the camera so that the whole cy...

Homotopy of exact coherent structures in plane shear flows

“…There are intriguing connections between critical Reynolds number values found here for steady states in plane Couette flow and physical experiments in much larger domains. 37 In fact, we believe that most of the characteristics of turbulence can be captured in relatively small periodic domains and that other features such as spots and ''barber pole'' structure 49 are ''secondary'' spatio-temporal complexities. Finally, it is most likely that the steady states and traveling wave solutions discussed here can be extended to traveling waves in pipe flow and to self-similar solutions in mixing layers.…”

A statistical study of spots in torsional Couette flow

“…Despite the extreme simplicity of this flow, its transition to turbulence is still an open question of fluid mechanics although recent important progresses have been realized. In particular Prigent et al (1) have shown that turbulence appears as periodic inclined bands in the laminar flow before it invades the whole flow. These bands whose origins and characteristics are not yet understood, have however been reproduced in numerical simulations by Barkley and Tuckerman (2).…”

Computational Study of Turbulent Laminar Patterns in Couette Flow

“…Due to its simplicity, this flow has long served as one of the canonical examples for understanding shear turbulence and the subcritical transition process typical of channel and pipe flows [1,2,3,4,5,6,7,8,9,10,11,12]. Only recently was it discovered in very large aspect ratio experiments by Prigent et al [13,14,15] that this flow also exhibits remarkable pattern formation near transition. Figure 1 shows such a pattern, not from experiment, but from numerical computations reported here.…”