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Nature of the Görtler Instability: A Forced Experiment

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The Global Geometry of Turbulence

Part of the book series: NATO ASI Series ((NSSB,volume 268))

Abstract

We study the instability of a concave boundary layer (Görtler instability) on a concave-convex model, in a water channel. Two different geometries were used either with (no streamwise pressure gradient) or without a counter-profile (favorable streamwise pressure gradient). In the first case Görtler vortices were present and randomly spaced. In the second case no vortex was detectable. The two flows exhibite different responses to localized forcings. We argue that these results may be interpreted by the non-linear convective instability concept, with a subcritical bifurcation when in presence of a favorable pressure gradient (accelerating flow).

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References

  1. M. Clauser and F. Clauser, The effect of curvature on the transition from laminar to turbulent boundary layer; Nat. Advisory Committee for Aeronautics, Techn. Note N°613, (1937).

    Google Scholar 

  2. H. Bippes and H. Gortler,Acta Mech. 14, 251 (1972).

    Article  Google Scholar 

  3. H. Görtler, Uber eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden, J. Rat. Mech. Anal.4, pp 271–321, (1955).

    Google Scholar 

  4. G. Hammerlin, Uber das Eigenwertproblem der dreidimensionalen Instabilität laminarer Grenzschichten an konkaven Wänden, J. Rat. Mech. Anal. Vol. 4, pp. 279–321 (1955).

    MathSciNet  Google Scholar 

  5. A. M. O. Smith, On the growth of Taylor-Görtler vortices along highly concave walls, Quart. Appl. Math. Vol. 13 n° 3, pp 233–262 (1955).

    MathSciNet  MATH  Google Scholar 

  6. M. J. Floryan, W. S. Saric, Stability of Görtler vortices in boundary layers,AIAA JournalVol. 20 n° 3, AIAA-19–1497R (1982).

    Google Scholar 

  7. S. A. Ragab, A. H. Nayfeh, Effect of pressure gradients on Görtler instability,Fluids 2 Plasma Dynamics Conference, AIAA-80–1377 (1980).

    Google Scholar 

  8. P. Hall, The linear development of Görtler vortices in growing boundary layers, J. Fluid Mech. 130, pp 41–58 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. P. Huerre, On the absolute:convective nature of primary and secondary instabilities.In Propagation in Systems Far from Equilibrium, ed. J. E. Weisfreid, H. R. Brand, P. Manneville, G. Albinet, N. Boccara, Berlin: Springer-Verlag pp 340–53 (1988).

    Chapter  Google Scholar 

  10. P. Huerre and P. A. Monkewitz, local and global instabilities in spatially developing flows,Annu. Rev. Fluid Mech. 22, 473 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  11. J. M. Chomaz, P. Huerre, L. G. Redekopp. Effect of nonlinearity and forcing on global modes, New Trends in Nonlinear Dyn. and Pattern-forming Phenom., ed P. Goulet, P. Huerrre, New York/London: Plenum (1990).

    Google Scholar 

  12. J. C. Buell, P. Huerre, Inflow/outflow boundary conditions and global dynamics of spatial mixing layers,Proc. NASA Ames/Stanford Cent. Turbul. Res. Summer Program. Rep. n° CTR-S88, pp 19–27 (1988).

    Google Scholar 

  13. D. S. Park and P. Huerre,preprint (1990).

    Google Scholar 

  14. J. M. Chomaz, Generalization of absolute and convective instability to non-linear systems,preprint (1990).

    Google Scholar 

  15. E. M. Lifshitz and L. P. Pitaevskii, Physical kinetics, Pergamon, Landau (1981).

    Google Scholar 

  16. R. J. Deissler, Noise-sustained structure, intermittency, and the Ginsburg-Landau equation, J. Stat. Phys.40: 371–95 (1985).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. M. Perrier, A. Butet, Veine hydraulique du CNRM fonctionnement en écoulement neutre,note de tray. EERM n°216 (1988).

    Google Scholar 

  18. H. Peerhossaini, H. Bippes and D. STEINBACH,preprint(1990).

    Google Scholar 

  19. H. Bippes, Experimental study of the laminar-turbulent transition on a concave wall in a parallel flow,NASATM-75243 (1978).

    Google Scholar 

  20. J. Andreopolous, W. Rodi, Experimental investigation of jets in a cross-flow, J. Fluid Mech. 138, 93–127 (1984).

    Article  ADS  Google Scholar 

  21. R. I. Sykes, W. S. Lewellen and S. F. Parker. On the vorticity dynamics of a turbulent jet in a crossflow, J. Fluid Mech. 168, 393–413 (1986).

    Article  ADS  MATH  Google Scholar 

  22. D. S. Needham, N. Riley and J. H. B. Smith, A jet in crossflow, J. Fluid Rech.188, 159–184 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. V. Kottke, Taylor-Görtler vortices and their effect on heat and mass transfer, proc. of 8th Int. Heat and transfer Conference, San Francisco (1986).

    Google Scholar 

  24. M. J. Floryan, W. S. Saric, Stability of Görtler vortices in boundary layers,AIAA JournalVol. 20 n° 3 AIAA-19–1497R (1982).

    Google Scholar 

  25. I. Tani, Y. Aihara, Görtler vortices and boundary layer transition, ZAMPVol. 20, pp 609–618 (1969).

    Article  ADS  Google Scholar 

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© 1991 Springer Science+Business Media New York

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Chomaz, J.M., Perrier, M. (1991). Nature of the Görtler Instability: A Forced Experiment. In: Jiménez, J. (eds) The Global Geometry of Turbulence. NATO ASI Series, vol 268. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3750-2_3

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  • DOI: https://doi.org/10.1007/978-1-4615-3750-2_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6670-6

  • Online ISBN: 978-1-4615-3750-2

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