Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T05:08:24.621Z Has data issue: false hasContentIssue false
  • English
  • Français

A new nonlinear vortex state in square-duct flow

Published online by Cambridge University Press:  01 July 2010

S. OKINO ,
M. NAGATA ,
H. WEDIN  and
A. BOTTARO
S. OKINO
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
M. NAGATA*
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
H. WEDIN
Affiliation:
Dipartimento di Ingegneria, delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Via Montallegro 1, 16145 Genoa, Italy
A. BOTTARO
Affiliation:
Dipartimento di Ingegneria, delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Via Montallegro 1, 16145 Genoa, Italy
*
†Email address for correspondence: nagata@kuaero.kyoto-u.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

A new nonlinear travelling-wave solution for a flow through an isothermal square duct is discovered. The solution is found by a continuation approach in parameter space, starting from a case where the fluid is heated internally. The Reynolds number for which the travelling wave emerges is much lower than that of the solutions discovered recently by an analysis based on the self-sustaining process (Wedin et al., Phys. Rev. E, vol. 79, 2009, p. 065305; Uhlmann et al., Advances in Turbulence XII, 2009, pp. 585–588). Furthermore, the new travelling-wave solution is shown to be unstable from the onset.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010 , pp. 413 - 429
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Biau, D. & Bottaro, A. 2009 An optimal path to transition in a duct. Phil. Trans. R. Soc. A 367, 529–544.CrossRefGoogle Scholar
Biau, D., Soueid, H. & Bottaro, A. 2008 Transition to turbulence in duct flow. J. Fluid Mech. 596, 133–142.CrossRefGoogle Scholar
Chapman, S. J. 2002 Subcritical transition in channel flows. J. Fluid Mech. 451, 35–97.CrossRefGoogle Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114.Google Scholar
Davey, A. & Drazin, P. G. 1969 The stability of Poiseuille flow in a pipe. J. Fluid Mech. 36 (2), 209–218.CrossRefGoogle Scholar
Duguet, Y., Willis, A. P. & Kerswell, R. R. 2008 Transition in pipe flow: the saddle structure on the boundary of turbulence. J. Fluid Mech. 613, 255–274.Google Scholar
Faisst, H. & Eckhardt, B. 2003 Traveling waves in pipe flow. Phys. Rev. Lett. 91, 224–502.CrossRefGoogle ScholarPubMed
Gavarini, M. I., Bottaro, A. & Nieuwstadt, F. T. M. 2005 Optimal and robust control of streaks in pipe flow. J. Fluid Mech. 537, 187–219.Google Scholar
Gavrilakis, S. 1992 Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 224, 101–129.Google Scholar
Generalis, S. C. & Nagata, M. 2003 Transition in homogeneously heated inclined plane parallel shear flows. J. Heat Trans. 125, 795–803.CrossRefGoogle Scholar
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244–502.Google Scholar
Huser, A. & Biringen, S. 1993 Direct numerical simulation of turbulent flow in a square duct. J. Fluid Mech. 257, 65–95.Google Scholar
Jones, O. C. 1976 An improvement in the calculation of turbulent friction in rectangular ducts. ASME J. Fluids Engng 98, 173–181.Google Scholar
Kawahara, G. & Kida, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291–300.Google Scholar
Kerswell, R. R. & Tutty, O. R. 2007 Recurrence of travelling waves in transitional pipe flow. J. Fluid Mech. 584, 69–102.Google Scholar
Nagata, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519–527.CrossRefGoogle Scholar
Pringle, C. C. T. & Kerswell, R. R. 2007 Asymmetric, helical and mirror-symmetric travelling waves in pipe flow. Phys. Rev. Lett. 99, 074502.Google Scholar
Pringle, C. C. T., Duguet, Y. & Kerswell, R. R. 2009 Highly symmetric travelling waves in pipe flow. Phil. Trans. R. Soc. A 367, 457–472.CrossRefGoogle ScholarPubMed
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and of the law of resistance in parallel channels. Phil. Trans. R. Soc. 174, 935–982.Google Scholar
Tatsumi, T. & Yoshimura, T. 1990 Stability of the laminar flow in a rectangular duct. J. Fluid Mech. 212, 437–449.CrossRefGoogle Scholar
Uhlmann, M. & Nagata, M. 2006 Linear stability of flow in an internally heated rectangular duct. J. Fluid Mech. 551, 387–404.CrossRefGoogle Scholar
Uhlmann, M., Pinelli, A., Kawahara, G. & Sekimoto, A. 2007 Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153–162.Google Scholar
Uhlmann, M., Kawahara, G. & Pinelli, A. 2009 Travelling waves in a straight square duct. In Advances in Turbulence XII (ed. Eckhardt, B.), In Proceedings of the 12th European Turbulence Conference, pp. 585–588. Springer.Google Scholar
Waleffe, F. 1998 Three-dimensional coherent states in plane shear flows. Phys. Rev. Lett. 81, 4140–4143.Google Scholar
Waleffe, F. 2001 Exact coherent structures in channel flow. J. Fluid Mech. 435, 93–102.CrossRefGoogle Scholar
Waleffe, F. 2003 Homotopy of exact coherent structures in plane shear flows. Phys. Fluids 15, 1517–1534.Google Scholar
Waleffe, F. & Wang, J. 2005 Transition threshold and the self-sustaining process. In IUTAM Symposium on Laminar–Turbulent Transition and Finite Amplitude Solutions (ed. Mullin, T. & Kerswell, R.), pp. 85–106. Springer.Google Scholar
Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333–371.CrossRefGoogle Scholar
Wedin, H., Biau, D., Bottaro, A. & Nagata, M. 2008 Coherent flow states in a square duct. Phys. Fluids 20, 094105.CrossRefGoogle Scholar
Wedin, H., Bottaro, A. & Nagata, M. 2009 Three-dimensional traveling waves in a square duct. Phys. Rev. E 79, 065305.CrossRefGoogle Scholar
Willis, A. P. & Kerswell, R. R. 2008 Coherent structures in localized and global pipe turbulence. Phys. Rev. Lett. 100, 124501.CrossRefGoogle ScholarPubMed