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A model of defect-induced pairing in mixing layers

Published online by Cambridge University Press:  26 April 2006

Ruixin Yang ,
Frederic K. Browand ,
Pierre Coullet  and
Patrick Huerre
Ruixin Yang
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA Present address: Institute for Computational Sciences & Informatics, George Mason University, Fairfax, VA 22030-4444, USA.
Frederic K. Browand
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
Pierre Coullet
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA Permanent address: Institut Nonlinéaire de Nice, Université de Nice, Parc Valrose, 06108 Nice, France.
Patrick Huerre
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA Present address: Laboratoire d’hydrodynamique (LADHYX), Ecole Polytechnique. 91128 Palaiseau Cedex, France.
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Abstract

Experiment have shown that the well-known vortex pairing process may take place first in defect regions where the fundamental structure is weakest. A model is introduced here to describe this defect-induced pairing process. The model is constructed in such a way that, in a certain parameter range, a stable fundamental mode and a stable subharmonic mode may coexist. The numerical simulation demonstrates that, when initial conditions consist of a dominant fundamental with one or more defects, the subharmonic component is preferentially generated in the cores of these defects. Moreover, the results also indicate that pairing may first commence wherever the fundamental mode is weakest provided the white-noise level of the subharmonic is high enough. The numerical results are in good agreement with experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 403 - 423
Copyright
© 1993 Cambridge University Press

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References

Balian, R., Klemann, M. & Poirier, J. 1981 Physics of Defects. Elsevier North-Holland.
Browand, F. K. & Prost-Domasky, S. 1990 Experiment on pattern evolution in the 2-d mixing layer. In New Trends in Nonlinear Dynamics and Patterning Phenomena: The Geometry of Nonequilibrium (ed. P. Coullet & P. Huerre). NATO ASI Series B, pp. 159– 169. Plenum.
Browand, F. K. & Troutt, T. R. 1980 A note on spanwise structure in the two-dimensional mixing layer. J. Fluid Mech. 97, 771– 781.Google Scholar
Browand, F. K. & Troutt, T. R. 1985 The turbulent mixing layer: geometry of large vortices. J. Fluid Mech. 158, 489– 509.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775– 816.Google Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatial-developing flows. Phys. Rev. Lett. 60, 25– 28.Google Scholar
Churilov, S. M. & Shukhman, I. G. 1987 Note on weakly nonlinear stability theory of a free mixing layer. Proc. R. Soc. Lond. A 409, 351– 367.Google Scholar
Coullet, P., Gil, L. & Repaux, D. 1989 Defects and subcritical bifurcations. Phys. Rev. Lett. 62, 2957– 2960.Google Scholar
Cross, M. C. 1988 Structure of nonlinear traveling-wave states in finite geometries. Phys. Rev. A 38, 3593– 3600.Google Scholar
Dallard, T. & Browand, F. K. 1993 The growth of large scales at defect sites in the plane mixing layer. J. Fluid Mech. 247, 339– 368.Google Scholar
Ho, C. M. & Huang, L. S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443– 473.Google Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365– 424.Google Scholar
Huerre, P. 1987 On the Landau constant in mixing layers. Proc. R. Soc. Lond. A 409, 369– 381.Google Scholar
Kelly, R. E. 1967 On the stability of an inviscid shear layer which is periodic in space and time. J. Fluid Mech. 27, 657– 689.Google Scholar
Kelly, R. E. 1968 On the resonant interaction of neutral disturbances in two inviscid shear flows. J. Fluid Mech. 31, 789– 799.Google Scholar
Lifshits, E. M. & Pitaevskii, L. P. 1981 Physical Kinetics. Pergamon.
Michalke, A. 1964 On the inviscid instability of the hyperbolic tangent velocity profile. J. Fluid Mech. 19, 543– 556.Google Scholar
Monkewitz, P. A. 1988 Subharmonic resonance, pairing and shedding in the mixing layer. J. Fluid Mech. 188, 223– 252.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237– 255.Google Scholar