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
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).
H. Bippes and H. Gortler,Acta Mech. 14, 251 (1972).
H. Görtler, Uber eine dreidimensionale Instabilität laminarer Grenzschichten an konkaven Wänden, J. Rat. Mech. Anal.4, pp 271–321, (1955).
G. Hammerlin, Uber das Eigenwertproblem der dreidimensionalen Instabilität laminarer Grenzschichten an konkaven Wänden, J. Rat. Mech. Anal. Vol. 4, pp. 279–321 (1955).
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).
M. J. Floryan, W. S. Saric, Stability of Görtler vortices in boundary layers,AIAA JournalVol. 20 n° 3, AIAA-19–1497R (1982).
S. A. Ragab, A. H. Nayfeh, Effect of pressure gradients on Görtler instability,Fluids 2 Plasma Dynamics Conference, AIAA-80–1377 (1980).
P. Hall, The linear development of Görtler vortices in growing boundary layers, J. Fluid Mech. 130, pp 41–58 (1983).
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).
P. Huerre and P. A. Monkewitz, local and global instabilities in spatially developing flows,Annu. Rev. Fluid Mech. 22, 473 (1990).
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).
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).
D. S. Park and P. Huerre,preprint (1990).
J. M. Chomaz, Generalization of absolute and convective instability to non-linear systems,preprint (1990).
E. M. Lifshitz and L. P. Pitaevskii, Physical kinetics, Pergamon, Landau (1981).
R. J. Deissler, Noise-sustained structure, intermittency, and the Ginsburg-Landau equation, J. Stat. Phys.40: 371–95 (1985).
M. Perrier, A. Butet, Veine hydraulique du CNRM fonctionnement en écoulement neutre,note de tray. EERM n°216 (1988).
H. Peerhossaini, H. Bippes and D. STEINBACH,preprint(1990).
H. Bippes, Experimental study of the laminar-turbulent transition on a concave wall in a parallel flow,NASATM-75243 (1978).
J. Andreopolous, W. Rodi, Experimental investigation of jets in a cross-flow, J. Fluid Mech. 138, 93–127 (1984).
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).
D. S. Needham, N. Riley and J. H. B. Smith, A jet in crossflow, J. Fluid Rech.188, 159–184 (1988).
V. Kottke, Taylor-Görtler vortices and their effect on heat and mass transfer, proc. of 8th Int. Heat and transfer Conference, San Francisco (1986).
M. J. Floryan, W. S. Saric, Stability of Görtler vortices in boundary layers,AIAA JournalVol. 20 n° 3 AIAA-19–1497R (1982).
I. Tani, Y. Aihara, Görtler vortices and boundary layer transition, ZAMPVol. 20, pp 609–618 (1969).
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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
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