Skip to main content

Strongly Nonlinear Oblique-Wave Solutions in Wall-Bounded Shear Flows

  • Conference paper
Nonlinear Instability of Nonparallel Flows

Abstract

Starting with a pair of symmetric oblique waves on the linear neutral surface, highly nonlinear 3D time-periodic equilibrium solutions were computed numerically for plane Poiseuille (PPF) and Blasius boundary-layer flow (BLF) via Keller’s pseudo-arclength continuation procedure. For BLF the parallel-flow assumption was used. This investigation was aimed at locating possible nonlinear thresholds for linear transient-growth solutions in bypass transition. For low-truncation PPF subcritical solutions were discovered near the experimentally observed minimum transition Reynolds number. Contrary to this, practically no subcritical primary equilibria were found in BLF, and the turbulent friction factor was approached only above a certain supercritical Reynolds number.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • ASAI, M. & NISHIOKA, M. 1990 Development of wall turbulence in Blasius flow. In IUTAM Symposium on Laminar-Turbulent Transition (eds. D. Arnal & R. Michel), pp.215–224. Springer.

    Google Scholar 

  • BOBERG, L. & BRÖSA, U. 1988 Onset of turbulence in a pipe. Z. Naturforsch. 43a, 697–726.

    Google Scholar 

  • BUTLER, K. M. & FARRELL, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637–1650.

    Article  ADS  Google Scholar 

  • CANUTO, C., HUSSAINI, M. Y., QUATERONI, A. & ZANG, T. A. 1988. Spectral Methods in Fluid Dynamics, Springer.

    Google Scholar 

  • CRAIK, A. D. D. 1985. Wave Interactions and Fluid Flows, Cambridge University Press.

    MATH  Google Scholar 

  • DHAWAN, S. 1953 Direct measurements of skin friction. NACA Rep. 1121.

    Google Scholar 

  • ELLINGSEN, T. & PALM, E. 1975 Stability of linear flow. Phys. Fluids 18, 487–488.

    Article  ADS  MATH  Google Scholar 

  • EHRENSTEIN, U. & KOCH, W. 1991 Three-dimensional wavelike equilibrium states in plane Poiseuille flow. J. Fluid Mech. 228 111–148.

    ADS  MATH  Google Scholar 

  • FARRELL, B. F. 1988 Optimal excitation of perturbations in viscous shear flow. Phys. Fluids 31 2093–2102.

    Article  ADS  Google Scholar 

  • HERBERT, TH. 1983 Secondary instability of plane channel flow to subharmonic three-dmensional disturbances. Phys. Fluids 26 871–874.

    Article  ADS  Google Scholar 

  • KEEFE, L. 1993 Drag reduction in channel flow using nonlinear control. AIAA paper 93–3279.

    Google Scholar 

  • KELLER, H. B. 1977 Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. P. H. Rabinowitz), pp. 359–384. Academic Press.

    Google Scholar 

  • KOCH, W. 1992 On a degeneracy of temporal secondary instability modes in Blasius boundary-layer flow. J. Fluid Mech. 243 319–351.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • PATEL, V. C. & HEAD, M. R. 1969 Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J. Fluid Mech. 38, 181–201.

    Article  ADS  Google Scholar 

  • REDDY, S. C. & HENNINGSON, D. S. 1993 Energy growth in viscous channel flows. J. Fluid Mech. (to appear).

    Google Scholar 

  • HENNINGSON, D. S., LUNDBLADH, A. & JOHANSSON, A. V. 1993 A mechanism for bypass transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250 169–207.

    Article  ADS  MATH  Google Scholar 

  • SCHMID, P. J. & HENNINGSON, D. S. 1992 A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids A 4, 1986–1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag, Berlin Heidelberg

About this paper

Cite this paper

Koch, W. (1994). Strongly Nonlinear Oblique-Wave Solutions in Wall-Bounded Shear Flows. In: Lin, S.P., Phillips, W.R.C., Valentine, D.T. (eds) Nonlinear Instability of Nonparallel Flows. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85084-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-85084-4_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85086-8

  • Online ISBN: 978-3-642-85084-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics