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On turbulent spots in plane Poiseuille flow

Published online by Cambridge University Press:  26 April 2006

Dan S. Henningson  and
John Kim
Dan S. Henningson
Affiliation:
Department of Mathematics, MIT, Cambridge MA 01239, USA
John Kim
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

Turbulence characteristics inside a turbulent spot in plane Poiseuille flow are investigated by analysing a database obtained from a direct numerical simulation. The spot is found to consist of two distinct regions — a turbulent area and a wave area. The flow inside the turbulent area has a strong resemblance to that found in the fully developed turbulent channel. Suitably defined mean and r.m.s. fluctuations as well as the internal shear-layer structures are found to be similar to the turbulent counterpart. In the wave area the inflexional mean spanwise profiles cause a rapid growth of oblique waves, which break down to turbulence. The breakdown process of the oblique waves is reminiscent of the secondary instability observed during transition to turbulence in channel and boundary-layer flows. Other detailed characteristics associated with the Poiseuille spot are presented and are compared with experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 228 , July 1991 , pp. 183 - 205
Copyright
© 1991 Cambridge University Press

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References

Alavyoon, F., Henningson, D. S. & Alfredsson, P. H. 1986 Turbulent spots in plane Poiseuille flow — flow visualization. Phys. Fluids 29, 1328–1331.Google Scholar
Bayly, B. J., Orszag, S. A. & Herbert, T. 1988 Instability mechanisms in shear-flow transition. Ann. Rev. Fluid Mech. 20, 359–391.Google Scholar
Blackwelder, R. F. & Kaplan, R. E. 1976 On the wall structure of the turbulent boundary layer. J. Fluid Mech. 76, 89–112.Google Scholar
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow visualization study of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487–505.Google Scholar
Chambers, F. W. & Thomas, A. S. W. 1983 Turbulent spots, wave packets and growth. Phys. Fluids 26, 1160–1162.Google Scholar
Elder, J. W. 1962 An experimental investigation of turbulent spots and breakdown to turbulence. J. Fluid Mech. 9, 235–246.Google Scholar
Emmons, H. W. 1951 The laminar-turbulent transition in boundary layer — part I. J. Aero. Sci. 18, 490–498.Google Scholar
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73–95.Google Scholar
Gaster, M. 1975 A theoretical model of a wave packet in the boundary layer of a flat plate.. Proc. R. Soc. Lond. A 347, 271–289.Google Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer.. Proc. R. Soc. Lond. A 347, 253–269.Google Scholar
Glezer, A., Katz, Y. & Wygnanski, I. 1989 On the breakdown of the wave packet trailing a turbulent spot in a laminar boundary layer. J. Fluid Mech. 198, 1–26.Google Scholar
Henningson, D. S. 1988 The inviscid initial value problem for a piecewise linear mean flow. Stud. Appl. Maths 78, 31–56.Google Scholar
Henningson, D. S. 1989 Wave growth and spreading of a turbulent spot in plane Poiseuille flow.. Phys. Fluids A 1, 1876–1882.Google Scholar
Henningson, D. S. & Alfredsson, P. H. 1987 The wave structure of turbulent spots in plane Poiseuille flow. J. Fluid Mech. 178, 405–421.Google Scholar
Henningson, D. S., Johansson, A. V. & Lundbladh, A. 1990 On the evolution of localized disturbances in laminar shear flows. In Laminar Turbulent Transition (ed. D. Arnal & R. Michel), pp. 279–284. Springer.
Henningson, D. S., Spalart, P. & Kin, J. 1987 Numerical simulations of turbulent spots in plane Poiseuille and boundary layers flows. Phys. Fluids 30, 2914–2917.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Ann. Rev. Fluid Mech. 20, 487–526.Google Scholar
Johannson, A. V., Alfredsson, P. H. & Km, J. 1991 Evolution and dynamics of shear-layer structures in near-well turbulence. J. Fluid Mech. 224, 579–599.Google Scholar
Johansson, A. V., Her, J. Y. & Haritonidis, J. H. 1987 On the generation of high-amplitude wall-pressure peaks in turbulent boundary layers and spots. J. Fluid Mech. 175, 119–142.Google Scholar
Kim, J. 1983 On the structure of wall bounded turbulent flows. Phys. Fluids 26, 2088–2097.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three dimensional nature of boundary layer transition. J. Fluid Mech. 12, 1–34.Google Scholar
Klingmann, B., Alfredsson, P. H. & Henningson, D. S. 1990 An experimental study of the velocity field of turbulent spots in plane Poiseuille flow. In Advances in Turbulence 2 (ed. H. E. Fielder & H. H. Fernholtz), pp. 9–14. Springer.
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in transition In Proc. 1962 Heat Transfer and Fluid Mechanics Institute, University of Washington, pp. 1–26.
Landahl, M. T. 1972 Wave mechanics of breakdown. J. Fluid Mech. 56, 775–802.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243–251.Google Scholar
Li, F. & Widnall, S. E. 1989 Wave patterns in plane Poiseuille flow created by concentrated disturbances. J. Fluid Mech. 208, 639–656.Google Scholar
Malkus, W. V. R. & Waleffe, F. A. 1991 The transition from order to disorder in elliptical flow: A direct path to shear flow turbulence. In Advances in Turbulence 3 (ed. A. V. Johansson & P. H. Alfredsson). Springer (to appear).
Maslowe, S. A. 1981 Shear flow instabilities and transition. In Hydrodynamic Instabilities and the Transition to Turbulence (ed. H. L. Swinney & J. P. Gollub), pp. 181–228. Springer.
Nishioka, N., Iida, S. & Ichikawa, Y. 1976 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731–751.Google Scholar
Orszag, S. A. & Patera, A. T. 1983 Secondary instability of wall-bounded shear flows. J. Fluid Mech. 128, 347–385.Google Scholar
Russell, J. M. & Landahl, M. T. 1984 The evolution of a flat eddy near a wall in an inviscid shear flow. Phys. Fluids 27, 557–570.Google Scholar
Schubauer, G. B. & Klebanoff, P. S. 1955 Contributions on the mechanics of boundary layer transition. NACA TN-3489.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Widnall, S. E. 1984 Growth of turbulent spots in plane Poiseuille flow. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 93–98. Elsevier.
Wygnanski, I., Haritonidis, J. H. & Kaplan, R. E. 1979 On a Tollmien–Schlichting wave packet produced by a turbulent spot. J. Fluid Mech. 92, 505–528.Google Scholar
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 On a turbulent spot in a laminar boundary layer. J. Fluid Mech. 78, 785–819.Google Scholar