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Experiments in rotating plane Couette flow – momentum transport by coherent roll-cell structure and zero-absolute-vorticity state

Published online by Cambridge University Press:  17 February 2016

Takuya Kawata  and
P. Henrik Alfredsson
Takuya Kawata*
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
P. Henrik Alfredsson
Affiliation:
Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: kawata@mech.kth.se
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Abstract

In spanwise rotating plane Couette flow (RPCF) a secondary flow dominated by three-dimensional roll-cell structures develops. At high enough rotation rates the flow exhibits a state of zero absolute vorticity at the centre of the channel, as described by Suryadi et al. (Phys. Rev. E, vol. 89, 2014, 033003). They suggested that the zero-absolute-vorticity state is caused by the secondary flow motion of the coherent roll-cell structure induced by the Coriolis force. In the present study we focus on the momentum transport caused by the roll-cell structure of laminar RPCF in order to further understand how the zero-absolute-vorticity state is maintained by the coherent roll cells. The flow is studied through stereoscopic particle image velocimetry measurements, which allow both the Reynolds shear stress and the wall shear stress to be quantified and used as measures of the momentum transport across the channel. Various types of roll-cell structures at different system rotation rates and the momentum transport induced by them are investigated, and the processes in which the momentum is transported in the wall-normal direction are discussed based on a displaced-particle argument as well as the production of the Reynolds stresses. It is shown that the wall-normal fluid motion driven by secondary flow of the roll-cell structure induces two different effects on the mean flow which conflict each other, the momentum transport in the wall-normal direction and the Coriolis acceleration, and the zero-absolute-vorticity state is a stable state where these two effects cancel each other.

JFM classification

Instability: Nonlinear instability Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , pp. 191 - 213
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Copyright
© 2016 Cambridge University Press 

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References

Alfredsson, P. H. & Tillmark, N. 2005 Instability, transition and turbulence in plane Couette flow with system rotation. In Proceedings of the IUTAM Symp., Non-Uniqueness of Solutions to the Navier–Stokes Equations and their Connection with Laminar–Turbulent Transition (ed. Mullin, T. & Kerswell, R.), pp. 173–193. Springer.Google Scholar
Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183.CrossRefGoogle Scholar
Bech, K. H. & Andersson, H. I. 1997 Turbulent plane Couette flow subject to strong system rotation. J. Fluid Mech. 347, 289–314.CrossRefGoogle Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177–191.CrossRefGoogle Scholar
Couliou, M. & Monchaux, R. 2015 Large-scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism. Phys. Fluids 27, 034101.CrossRefGoogle Scholar
Daly, C. A., Schneider, T. M., Schlatter, P. & Peake, N. 2014 Secondary instability and tertiary states in rotating plane Couette flow. J. Fluid Mech. 761, 27–61.CrossRefGoogle Scholar
Daviaud, F., Hegseth, J. & Bergé, P. 1992 Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett. 69, 2511–2514.CrossRefGoogle ScholarPubMed
Hagiwara, Y., Sakamoto, S., Tanaka, M. & Yoshimura, K. 2002 PTV measurement on interaction between two immiscible droplets and turbulent uniform shear flow of carrier fluid. Exp. Therm. Fluid Sci. 26, 245–252.CrossRefGoogle Scholar
Hiwatashi, K., Alfredsson, P. H., Tillmark, N. & Nagata, M. 2007 Experimental observations of instabilities in rotating plane Couette flow. Phys. Fluids 19, 048103.CrossRefGoogle Scholar
Kloosterziel, R. C., Orlandi, P. & Carnevale, G. F. 2007 Saturation of inertial instability in rotating planar shear flows. J. Fluid Mech. 583, 413–422.CrossRefGoogle Scholar
Kristoffersen, R. & Andersson, H. I. 1993 Direct simulations of low-Reynolds-number turbulent flow in a rotating channel. J. Fluid Mech. 256, 163–197.CrossRefGoogle Scholar
Lezius, D. K. & Johnston, J. P. 1976 Roll-cell instabilities in rotating laminar and turbulent channel flows. J. Fluid Mech. 77, 153–175.CrossRefGoogle Scholar
Malerud, S., LØY, K. J. Må & Goldburg, W. I. 1995 Measurements of turbulent velocity fluctuations in a planar Couette cell. Phys. Fluids 7, 1949–1955.CrossRefGoogle Scholar
Nagata, M. 1998 Tertiary solutions and their stability in rotating plane Couette flow. J. Fluid Mech. 358, 357–378.CrossRefGoogle Scholar
Prandtl, L. 1925 Über die ausgebildete Turbulenz. Z. Angew. Math. Mech. 5, 136–138.CrossRefGoogle Scholar
Soloff, S. M., Adrian, R. J. & Liu, Z.-C. 1997 Distortion compensation for generalized stereoscopic particle image velocimetry. Meas. Sci. Technol. 8, 1441–1454.CrossRefGoogle Scholar
Suryadi, A., Segalini, A. & Alfredsson, P. H. 2014 Zero absolute vorticity: insight from experiments in rotating laminar plane Couette flow. Phys. Rev. E 89, 033003.CrossRefGoogle ScholarPubMed
Suryadi, A., Tillmark, N. & Alfredsson, P. H. 2013 Velocity measurements of streamwise roll cells in rotating plane Couette flow. Exp. Fluids 54, 1617.CrossRefGoogle Scholar
Tanaka, M., Kida, S., Yanase, S. & Kawahara, G. 2000 Zero-absolute-vorticity state in a rotating turbulent shear flow. Phys. Fluids 12, 1979–1985.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1991 An experimental study of transition in plane Couette flow. In Advances in Turbulence 3 (ed. Johansson, A. V. & Alfredsson, P. H.), pp. 235–242. Springer.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1996 Experiments on rotating plane Couette flow. In Advances in Turbulence VI (ed. Gavrilakis, S., Machiels, L. & Monkewitz, P. A.), pp. 391–394. Kluwer.CrossRefGoogle Scholar
Tritton, D. J. & Davies, P. A. 1985 Instabilities in geophysical fluid dynamics. In Hydrodynamic Instabilities and the Transition to Turbulence, 2nd edn. (ed. Swinney, H. L. & Gollub, J. P.), Topics in Applied Physics, vol. 45, pp. 229–270. Springer.CrossRefGoogle Scholar
Tsukahara, T., Tillmark, N. & Alfredsson, P. H. 2010 Flow regimes in a plane Couette flow with system rotation. J. Fluid Mech. 648, 5–33.CrossRefGoogle Scholar
Wereley, S. & Gui, L. 2003 A correlation-based central difference image correction (CDIC) method and application in a four-roll mill flow PIV measurement. Exp. Fluids 34, 42–51.CrossRefGoogle Scholar
Wilcox, D. C. 1993 Turbulence Modeling for CFD. DCW Industries, Inc.Google Scholar
Xia, Z., Shi, Y. & Chen, S. 2016 Direct numerical simulation of turbulent channel flow with spanwise rotation. J. Fluid Mech. 788, 42–56.CrossRefGoogle Scholar
Zettner, C. M. & Yoda, M. 2001 The circular cylinder in simple shear at moderate Reynolds numbers: an experimental study. Exp. Fluids 30, 246–353.CrossRefGoogle Scholar