Hostname: page-component-5b777bbd6c-v47t2 Total loading time: 0 Render date: 2025-06-20T02:17:53.582Z Has data issue: false hasContentIssue false
  • English
  • Français

The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow

Published online by Cambridge University Press:  20 April 2006

G. M. Corcos  and
F. S. Sherman
G. M. Corcos
Affiliation:
University of California, Berkeley, CA 94720
F. S. Sherman
Affiliation:
University of California, Berkeley, CA 94720
Get access Rights & Permissions [Opens in a new window]

Abstract

The prevalence in a turbulent mixing layer of dynamical events with a coherent history over substantial times suggests that it is profitable to study in detail entirely deterministic versions of this flow and to attempt to use a simplified synthesis of these solutions as the fundamental representation in a stochastic treatment of the layer. It is proposed that the deterministic representation of the flow be achieved by the embedding of a short hierarchy of motions which are studied in detail, though not exhaustively, in Parts 1, 2 and 3. Part 1 deals with the fundamental or first-order motion, which is the evolution of a layer constrained to be purely two-dimensional.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 29 - 65
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Acton, E. 1976 J. Fluid Mech. 76, 561.
Amsden, A. A. & Harlow, F. H. 1964 Phys. Fluids 7, 327.
Ashurst, W. T. 1979 Numerical simulation of turbulent mixing layers via vortex dynamics. In Turbulent Shear Flow I (ed. F. Durst et al., p. 402. Springer.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Batt, R. G. 1975 Some measurements on the effect of tripping the two-dimensional shear layer AIAA J. 13, 245.Google Scholar
Beale, T. J. & Majda, A. 1981 Math. Comp. 37, 243.
Beale, T. J. & Majda, A. 1982 Math. Comp. 39, 29.
Brachet, M. E. & Orszag, S. 1982 Secondary instability of free shear layer flows. Submitted to J. Fluid Mech.Google Scholar
Bradshaw, P. 1966 J. Fluid Mech. 26, 225.
Breidenthal, R. E. 1978 A chemically reacting shear layer. Thesis. Calif. Inst. Tech.
Browand, F. K. 1966 J. Fluid Mech. 26, 281.
Browand, F. K. & Ho, C. M. 1983 The mixing layer: an example of quasi-two-dimensional turbulence. J. Méc. Théor. Appl. (to appear).Google Scholar
Browand, F. K. & Latigo, B. O. 1979 Phys. Fluids 22, 1011.
Browand, F. K. & Troutt, T. R. 1980 J. Fluid Mech. 97, 771.
Browand, F. K. & Weidman, D. D. 1976 J. Fluid Mech. 76, 127.
Brown, G. L. & Roshko, A. 1974 J. Fluid Mech. 64, 775.
Cantwell, B. J. 1981 Ann. Rev. Fluid Mech. 13, 457–457.
Chorin, A. J. 1973 J. Fluid Mech. 57, 785.
Chorin, A. J. 1978 J. Comp. Phys. 27, 428.
Chorin, A. J., Hughes, T. J. R., Mccracken, M. F. & Marsden, J. E. 1978 Commun. Pure Appl. Maths 31, 205.
Christiansen, J. P. 1973 J. Comp. Phys. 13, 363.
Corcos, G. M. 1979 The mixing layer: deterministic model of a turbulent flow. Univ. Calif., Berkeley, Coll. Engng Rep. FM-79–2.Google Scholar
Corcos, G. M. 1981 The deterministic description of the coherent structure of free shear layers. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, p. 10. Springer.
Corcos, G. M. & Lin, S. J. 1984 J. Fluid Mech. 139, 67.
Corcos, G. M. & Sherman, F. S. 1976 J. Fluid Mech. 73, 241.
Corrsin, S. 1962 Phys. Fluids 5, 1301.
Corrsin, S. & Kistler, A. L. 1954 NACA. TN 3133.
Deem, G. S. 1977 The origin of cusped waves in layered fluids (unpublished).
Delcourt, B. A. G. & Brown, G. L. 1979 The evolution and emerging structure of a vortex sheet in an inviscid and viscous fluid modelled by a point vortex method. In Proc. 2nd Symp. on Turbulent Shear Flows, July 1979, Imperial Coll., London, p. 14.35.Google Scholar
Dimotakis, P. E., MIAKE-LYE, R. C. & Papantoniou, D. A. 1982 J. Fluid Mech. 73, 241.
Drazin, P. & Reid, W. 1981 Hydrodynamic Stability. Cambridge University Press.
Freymuth, P. 1966 J. Fluid Mech. 25, 683.
Guiraud, J. P. & Zeytounian, R. KH. 1977 J. Fluid Mech. 25, 683.
Guiraud, J. P. & Zeytounian, R. KH. 1979 J. Fluid Mech. 90, 197.
Hald, O. H. 1979 SIAM J. Numer. Anal. 16, 726.
Ho, C. M. & Huang, L. S. 1982 J. Fluid Mech. 119, 443.
Hussain, A. K. M. F. 1980 Coherent structures and studies of perturbed and unperturbed jets. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, p. 252. Springer.
Hussain, A. K. M. F. & Clark, A. R. 1981 J. Fluid Mech. 104, 263.
Jimenez, J. 1980 J. Fluid Mech. 96, 447.
Jimenez, J., MARTINEZ-VAL, R. & Herman, M. A. 1981 Shear layer models and computer analysis of data. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, p. 41. Springer.
Kaul, U. K. 1982 Do large vortices control their own growth in a mixing layer? An assessment by a boot-strap method. Ph.D. thesis, Univ. Calif., Berkeley, Mech. Engng Dept.
Kelly, R. E. 1967 J. Fluid Mech. 27, 657.
Konrad, J. H. 1977 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Thesis, Calif. Inst. Tech.
Koop, C. G. & Browand, F. K. 1979 J. Fluid Mech. 93, 135.
Lamb, H. 1932 Hydrodynamics. Dover.
Latigo, B. 1979 Large-scale structure interactions in a two-dimensional turbulent mixing layer. Ph.D. thesis, Dept. Aero-space Engng, Univ. S. Calif., Los Angeles.
Laufer, J. & Mankovitz, P. 1980 AIAA Paper 80–8062.
Leonard, A. 1980 Vortex methods for flow simulation. Ames Res. Center. NASA Rep.Google Scholar
Liepmann, H. W. & Laufer, J. 1949 Investigation of free turbulent mixing. NACATN 1257.Google Scholar
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 stretched vortices. J. Fluid Mech. (to be published).Google Scholar
Marble, F. E. 1983 Growth of a diffusion flame in the field of a vortex. To appear in the Luigi Crocco anniversary volume.
Moore, D. W. 1976 Mathematica 23, 35.
Moore, D. W. & Saffman, P. G. 1975 J. Fluid Mech. 69, 465.
Neu, J. 1984a The evolution of diffusion flames convected by vortices. Submitted to J. Fluid Mech.Google Scholar
Neu, J. 1984b The dynamics of stretched vortices. J. Fluid Mech. (to be published).Google Scholar
Overman, E. A. Ii & Zabusky, N. J. 1981 Evolution and merger of isolated vortex structures. Univ. Pittsburgh, Tech. Rep. ICMA 81–31.Google Scholar
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 J. Fluid Mech. 73, 215.
Peltier, W. R., HALLÉ, J. & Clark, T. L. 1978 Geophys. Astrophy. Fluid Dyn. 10, 53.
Pierrehumbert, R. T. & Widnall, S. E. 1981 J. Fluid Mech. 102, 301.
Pierrehumbert, R. T. & Widnall, S. E. 1982 J. Fluid Mech. 114, 59.
Pui, N. K. & Gartshore, I. 1978 J. Fluid Mech. 91, 111.
Riley, J. J. & Metcalfe, R. W. 1980 Direct numerical simulation of a perturbed turbulent mixing layer. AIAA 18th Aerospace Meeting, Pasadena, CA: AIAA Reprint 80–0274.Google Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. Dryden Lecture. AIAA Reprint 76–78.Google Scholar
Saffman, P. G. 1968 Lectures on Homogeneous Turbulence. In Topics on Non-Linear Physics (ed. N. Zabusky), p. 485. Springer.
Sato, H. 1956 Experimental investigations of the transition of laminar separated layer J. Phys. Soc. Japan 11, 702.Google Scholar
Sherman, F. S. 1979 User's guide to program Khint. Univ. Calif. Rep., Dept. Mech. Engng.Google Scholar
Stuart, J. T. 1967 J. Fluid Mech. 29, 417.
Synge, J. L. & Lin, C. C. 1943 Trans. R. Soc. Canada 37, 45.
Tanaka, H. 1975 J. Met. Soc. Japan 53, 1.
Tennekes, H. 1968 Phys. Fluids 11, 669.
Thorpe, S. A. 1971 J. Fluid Mech. 46, 289.
Townsend, A. A. 1951 Proc. R. Soc. Lond. A, 208, 534.
Van Dyke, M. 1982 Album of Fluid Motion. Parabolic.
Wille, R. 1963 Growth of velocity fluctuations leading to turbulence in a free shear layer flow. Rep. AFOSR-TR-AF 61 (52), p. 412.Google Scholar
Winant, C. D. & Browand, F. K. 1974 J. Fluid Mech. 63, 237.
Wygnanski, I. & Fiedler, H. E. 1970 J. Fluid Mech. 41, 327.
Wygnanski, I., Oyster, D., Fiedler, H. & Dziomba, B. 1979 J. Fluid Mech. 93, 325.
Zabusky, N. J. 1981 Ann. NY Acad. Sci. 373, 160.
Zabusky, N. J. & Deem, G. G. 1971 J. Fluid Mech. 47, 353.
Zabusky, N. J., Hughes, M. H. & Roberts, K. V. 1979 J. Comp. Phys. 30, 96.
Zabusky, N. J. & Overman, E. A. 1981 Regularization of contour dynamical algorithms. Univ. Pittsburgh Tech. Rep. ICMA 81–22.Google Scholar