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Direct numerical simulation of spiral turbulence

Published online by Cambridge University Press:  13 December 2010

S. DONG  and
X. ZHENG
S. DONG*
Affiliation:
Center for Computational and Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
X. ZHENG
Affiliation:
Center for Computational and Applied Mathematics, Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we present results of three-dimensional direct numerical simulations of the spiral turbulence phenomenon in a range of moderate Reynolds numbers, in which alternating intertwined helical bands of turbulent and laminar fluids co-exist and propagate between two counter-rotating concentric cylinders. We show that the turbulent spiral is comprised of numerous small-scale azimuthally elongated vortices, which align into and collectively form the barber-pole-like pattern. The domain occupied by such vortices in a plane normal to the cylinder axis resembles a ‘crescent moon’, a shape made well known by Van Atta with his experiments in the 1960s. The time-averaged mean velocity of spiral turbulence is characterized in the radial–axial plane by two layers of axial flows of opposite directions. We also observe that, as the Reynolds number increases, the transition from spiral turbulence to featureless turbulence does not occur simultaneously in the whole domain, but progresses in succession from the inner cylinder towards the outer cylinder. Certain aspects pertaining to the dynamics and statistics of spiral turbulence and issues pertaining to the simulation are discussed.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 150 - 173
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

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.Google Scholar
Barkley, D. & Tuckerman, L. S. 2005 Computational study of turbulent laminar patterns in Couette flow. Phys. Rev. Lett. 94, 014502.Google Scholar
Barkley, D. & Tuckerman, L. S. 2007 Mean flow of turbulent–laminar patterns in plane Couette flow. J. Fluid Mech. 576, 109–137.Google Scholar
Berge, P., Pomeau, Y. & Vidal, C. 1984 Order Within Chaos. Wiley.Google Scholar
Bottin, S., Daviaud, F., Manneville, P. & Dauchot, O. 1998 Discontinuous transition to spatiotemporal intermittency in plane Couette flow. Europhys. Lett. 43, 171–176.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385–425.CrossRefGoogle Scholar
Coles, D. & Van Atta, C. 1966 Progress report on a digital experiment in spiral turbulence. AIAA J. 4, 1969–1971.CrossRefGoogle Scholar
Coles, D. & VanAtta, C. Atta, C. 1967 Digital experiment in spiral turbulence. Phys. Fluids Suppl. pp. S120–S121.Google Scholar
Colovas, P. W. & Andereck, C. D. 1997 Turbulent bursting and spatiotemporal intermittency in the counter-rotating Taylor–Couette system. Phys. Rev. E 55, 2736–2741.Google Scholar
Coughlin, K. & Marcus, P. S. 1996 Turbulent bursts in Couette–Taylor flow. Phys. Rev. Lett. 77, 2214–2217.Google Scholar
Cros, A. & Gal, P. Le 2002 Spatiotemporal intermittency in the torsional Couette flow between a rotating and a stationary disk. Phys. Fluids 14, 3755–3765.Google Scholar
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.CrossRefGoogle Scholar
Dong, S. 2007 Direct numerical simulation of turbulent Taylor–Couette flow. J. Fluid Mech. 587, 373–393.Google Scholar
Dong, S. 2008 Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study. J. Fluid Mech. 615, 371–399.Google Scholar
Dong, S. 2009 a Direct numerical simulation of spiral turbulence. In 16th International Couette-Taylor Workshop. Princeton, NJ.Google Scholar
Dong, S. 2009 b Evidence for internal structures of spiral turbulence. Phys. Rev. E 80, 067301.Google ScholarPubMed
Dong, S. & Karniadakis, G. E. 2004 Dual-level parallelism for high-order CFD methods. Parallel Comput. 30, 1–20.CrossRefGoogle Scholar
Dong, S. & Karniadakis, G. E. 2005 DNS of flow past a stationary and oscillating cylinder at Re = 10 000. J. Fluid Struct. 20, 519–531.Google Scholar
Dong, S., Karniadakis, G. E., Ekmekci, A. & Rockwell, D. 2006 A combined direct numerical simulation-particle image velocimetry study of the turbulent near wake. J. Fluid Mech. 569, 185–207.Google Scholar
Dong, S., Karniadakis, G. E. & Karonis, N. T. 2005 Cross-site computations on the TeraGrid. Comput. Sci. Engng 7, 14–23.Google Scholar
Eckhardt, B., Grossmann, S. & Lohse, D. 2007 Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J. Fluid Mech. 581, 221–250.CrossRefGoogle Scholar
Feynman, R. P. 1964 Lectures in Physics, vol. 2. Addison-Wesley.Google Scholar
Goharzadeh, A. & Mutabazi, I. 2001 Experimental characterization of intermittency regimes in the Couette–Taylor system. Eur. Phys. J. B 19, 157–162.CrossRefGoogle Scholar
Goharzadeh, A. & Mutabazi, I. 2008 The phase dynamics of spiral turbulence in the Couette–Taylor system. Eur. Phys. J. B 66, 81–84.Google Scholar
Hegseth, J. J. 1996 Turbulent spots in plane Couette flow. Phys. Rev. E 54, 4915–4923.Google Scholar
Hegseth, J. J., Andereck, C. D., Hayot, F. & Pomeau, Y. 1989 Spiral turbulence and phase dynamics. Phys. Rev. Lett. 62, 257–260.CrossRefGoogle ScholarPubMed
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97, 414–443.Google Scholar
Lepiller, V., Prigent, A., Dumouchel, F. & Mutabazi, I. 2007 Transition to turbulence in a tall annulus submitted to a radial temperature gradient. Phys. Fluids 19, 054101.CrossRefGoogle Scholar
Litschke, H. & Roesner, K. G. 1998 New experimental methods for turbulent spots and turbulent spirals in the Taylor–Couette flow. Exp. Fluids 24, 201–209.CrossRefGoogle Scholar
Marques, F., Meseguer, A., Mellibovsky, F. & Avila, M. 2009 Spiral turbulence in counter-rotating Taylor–Couette flow. In 16th International Couette–Taylor Workshop. Princeton, NJ.Google Scholar
Meseguer, A., Mellibovsky, F., Avila, M. & Marques, F. 2009 Instability mechanisms and transition scenarios of spiral turbulence in Taylor–Couette flow. Phys. Rev. E 80, 046315.Google Scholar
Prigent, A., Gregoire, G., Chate, H., Dauchor, O. & Van Saarloos, W. 2002 Large-scale finite-wavelength modulation with turbulent shear flows. Phys. Rev. Lett. 89, 014501.CrossRefGoogle ScholarPubMed
Prigent, A., Gregoire, G., Chate, H. & Dauchot, O. 2003 Long-wavelength modulation of turbulent shear flows. Physica D 174, 100–113.Google Scholar
Van Atta, C. 1966 Exploratory measurements in spiral turbulence. J. Fluid Mech. 25, 495–512.Google Scholar