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The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence

Published online by Cambridge University Press:  26 April 2006

Robert D. Moser
Affiliation:
NASA-Ames Research Center, Moffett Field, CA 94035, USA
Michael M. Rogers
Affiliation:
NASA-Ames Research Center, Moffett Field, CA 94035, USA

Abstract

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Type
Research Article
Copyright
© 1993 Cambridge University Press

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References

Bernal, L. P. 1981 The coherent structure of turbulent mixing layers. Ph.D. thesis, California Institute of Technology.
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499525.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 124.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775816.Google Scholar
Buell, J. C. & Mansour, N. N. 1989 Asymmetric effects in three-dimensional spatially-developing mixing layers. In Proc. Seventh Intl Symp. on Turbulent Shear Flows, Stanford University, Stanford, CA, pp. 9.2.19.2.6.
Buell, J. C., Moser, R. D. & Rogers, M. M. 1992 A comparison of spatially and temporally developing mixing layers. (In preparation.)
Burke, S. P. & Schumann, T. E. W. 1928 Diffusion flames. Ind. Engng Chem. 20, 9981004.Google Scholar
Corcos, G. M. & Lin, S. J. 1984 The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion. J. Fluid Mech. 139, 6795.Google Scholar
Corcos, G. M. & Sherman, F. S. 1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow. J. Fluid Mech. 139, 2965.Google Scholar
Hernan, M. A. & Jimenez, J. 1982 Computer analysis of a high-speed film of the plane turbulent mixing layer. J. Fluid Mech. 119, 323345.Google Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443473.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365424.Google Scholar
Huang, L.-S. & Ho, C.-M. 1990 Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475500.Google Scholar
Jimenez, J. 1983 A spanwise structure in the plane shear layer. J. Fluid Mech. 132, 319336.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, 657689.Google Scholar
Konrad, J. H. 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Internal Rep. CIT-8-PU. Calif. Inst. Technol. Pasadena, CA.
Koochesfahani, M. M. & Dimotakis, P. E. 1986 Mixing and chemical reactions in a turbulent liquid mixing layer. J. Fluid Mech. 170, 83112.Google Scholar
Lasheras, J. C., Cho, J. S. & Maxworthy, T. 1986 On the origin and evolution of streamwise vortical structures in a plane, free shear layer. J. Fluid Mech. 172, 231258.Google Scholar
Lasheras, J. C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 5386.CrossRefGoogle Scholar
Lele, S. K. 1989 Direct numerical simulation of compressible free shear flows. AIAA Paper 89–0374.
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139178.CrossRefGoogle Scholar
Lowery, P. S. & Reynolds, W. C. 1986 Numerical simulation of a spatially-developing, forced, plane mixing layer. Dept. Mech. Engng Rep. TF-26. Stanford University, Stanford. California.
Martel, C., Mora, E. & Jimenez, J. 1989 Small scales generation in 2-D mixing layers. Bull. Am. Phys. Soc. 34, 2268.Google Scholar
Metcalfe, R. W., Orszag, S. A., Brachet, M. E., Menon, S. & Riley, J. J. 1987 Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184, 207243.Google Scholar
Monkewitz, P. A. 1988 Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech. 188, 223252.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 Influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 11371143.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The density of organized vortices in a turbulent mixing layer. J. Fluid Mech. 69, 465473.Google Scholar
Moser, R. D. & Rogers, M. M. 1991 Mixing transition and the cascade to small scales in a plane mixing layer. Phys. Fluids A 3, 11281134.Google Scholar
Moser, R. D. & Rogers, M. M. 1992 The three-dimensional evolution of a plane mixing layer Part 2: Pairing and transition to turbulence. NASA TM 103926.
Nygaard, K. J. & Glezer, A. 1991 Evolution of streamwise vortices and generation of small-scale motion in a plane mixing layer. J. Fluid Mech. 231, 257301.Google Scholar
Oster, D. & Wygnanski, I. 1982 The forced mixing layer between parallel streams. J. Fluid Mech. 123, 91130.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E. 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 59 82.Google Scholar
Riley, J. J. & Metcalfe, R. W. 1980 Direct numerical simulation of a perturbed turbulent mixing layer. AIAA Paper 80-0274.
Rogers, M. M. & Moser, R. D. 1991 The three-dimensional evolution of a plane mixing layer Part 1. The Kelvin–Helmholtz roll-up. NASA TM 103856.
Rogers, M. M. & Moser, R. D. 1992 The three-dimensional evolution of a plane mixing layer: the Kelvin–Helmholtz rollup. J. Fluid Mech. 243, 183226 (referred to herein as RM).Google Scholar
Rogers, M. M. & Moser, R. D. 1993 Spanwise scale selection in plane mixing layers. J. Fluid Mech. 247, 321337.Google Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96, 297324.Google Scholar
Stuart, J. T. 1967 On finite amplitude oscillations in laminar mixing layers. J. Fluid Mech. 29, 417440.Google Scholar
Toor, H. L. 1962 Mass transfer in dilute turbulent and non-turbulent systems with rapid irreversible reactions and equal diffusivities. AIChE J. 8, 7078.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, 237255.Google Scholar
Yang, Z. & Karlsson, S. K. F. 1991 Evolution of coherent structures in a plane shear layer. Phys. Fluids A 3, 22072219.Google Scholar
Zeldovich, Y. B. 1951 On the theory of combustion of initially unmixed gases. NACA TM 1296.