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Do large structures control their own growth in a mixing layer? An assessment

Published online by Cambridge University Press:  21 April 2006

Upender K. Kaul
Upender K. Kaul
Affiliation:
Sterling Federal Systems (Palo Alto), NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

This study makes a specific comparison between two different two-dimensional free shear layers: the T-layer which develops in time from an initial tangential velocity discontinuity separating the two half-spaces; and the S-layer which develops downstream of the origin where two uniform streams of unequal velocity are brought into tangential contact. The method of comparison is to assume that the vorticity of the S-layer is given parabolically by a Galilean mapping of that of the T-layer; to satisfy the appropriate boundary conditions in the S-layer and to compute the velocity induced at any point in the S-layer by its vorticity field; and to compare this velocity to that which can be derived from the velocity of the T-layer at corresponding points by a Galilean transformation of the velocity itself. The purpose of this calculation is to assess approximately how far the flow in the S-layer is from parabolic and, in particular, to what extent the perturbations induced upstream by large concentrations of vorticity found downstream are instrumental in hastening or retarding the subharmonic instability that leads to the formation of these large structures. The calculations suggest that this elliptic influence, or the feedback, in a mixing layer is relatively small, at least for small velocity ratios.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 190 , May 1988 , pp. 427 - 450
Copyright
© 1988 Cambridge University Press

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References

Ashurst, W. T. 1977 Numerical simulation of turbulent mixing layers via vortex dynamics. In Turbulent Shear Flows (ed. F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), p. 402. Springer.
Batt, R. G. 1975 Some measurements on the effect of tripping the two-dimensional shear layer. AIAA J. 2, 245.Google Scholar
Browand, F. K. 1966 An experimental investigation of an incompressible, separated shear layer. J. Fluid Mech. 26, 281.Google Scholar
Brown, G. R. & Roshko, A. 1974 On the density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775.Google Scholar
Bradshaw, P. 1966 The effect of initial conditions on the development of a free shear layer. J. Fluid Mech. 26, 225.Google Scholar
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 785.Google Scholar
Coles, D. 1985 On the uses of coherent structures. AIAA Dryden Lecture, 23rd AIAA Aerospace Sciences Meeting, January, Reno, Nevada.
Corcos, G. M. 1979 The mixing layer: deterministic models of a turbulent flow, Rep. FM-79-2. University of California, Berkeley.
Corcos, G. M. 1980 The deterministic description of the coherent structure of free shear layers. Intl Conf. on Coherent Structure in Turbulent Shear Flow, Madrid, Spain. Lecture Notes in Physics, vol. 136, p. 10, Springer.
Corcos, G. M. & Sherman, F. S. 1976 Vorticity concentration and the dynamics of unstable free-shear layers. J. Fluid Mech. 73, 241.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, 29.Google Scholar
Davis, R. W. & Moore, E. F. 1985 A numerical study of vortex merging in mixing layers. Phys. Fluids 28, 1626.Google Scholar
Dimotakis, P. E. & Brown, G. L. 1976 The mixing layer at high Reynolds number: large-structure dynamics and entrainment. J. Fluid Mech. 78, 535.Google Scholar
Favre, A., Gaviglio, J. & Dumas, R. 1967 Structure of velocity space–time correlations in a boundary layer. Phys. Fluids 10, S138.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683.Google Scholar
Fujiwara, T., Taki, S. & Arashi, K. 1986 Numerical analysis of a reacting flow in H2/O2 rocket combustor. Part 1: Analysis of turbulent shear flow. AIAA Paper 86–0528, AIAA 24th Aerospace Sciences Meeting, January 1986.
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222.Google Scholar
Gaster, M. 1965 The role of spatially growing waves in the theory of hydrodynamic stability. Prog. Aero. Sci. 6, 251.Google Scholar
Ho, C.-M. & Huang, L.-S. 1982 Subharmonics and vortex merging in mixing layers. J. Fluid Mech. 119, 443.Google Scholar
Jiménez, J. 1980 On the visual growth of a turbulent mixing layer. J. Fluid Mech. 96, 447.Google Scholar
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, University of California, Berkeley, Mech. Engng Dept.
Kaul, U. K. 1986a A numerical method to assess the feedback in a free shear layer. In Proc. Tenth Intl Conf. on Numerical Methods in Fluid Dynamics, Beijing, China, June 23–27. Lecture Notes in Physics, vol. 264, p. 369, Springer.
Kaul, U. K. 1986b A computational study of the subharmonic instability in mixing layers. Proc. Tenth US National Congress of Applied Mechanics, The University of Texas at Austin, Austin, Texas, June 16–20 (ed. J P. Lamb), p. 545. ASME.
Kibens, V. 1980 Discrete noise spectrum generated by an acoustically excited jet. AIAA J. 18, 434.Google Scholar
Laufer, J. & Monkewitz, P. 1980 On turbulent jet flows: a new perspective. AIAA Paper 80–0962.
Liepman, H. W. & Laufer, J. 1947 Investigation of free turbulent mixing. NACA Tech. Note 1257.
Miles, J. B. & Shih, J. 1968 Similarity parameter for two-stream turbulent jet-mixing region. AIAA J. 6, 1429.Google Scholar
Mills, R. D. 1968 Numerical and experimental investigations of the shear layer between two parallel streams. J. Fluid Mech. 33, 591.Google Scholar
Monkewitz, P. A. & Huerre, P. 1982 The influence of the velocity ratio on the spatial instability of mixing layers. Phys. Fluids 25, 1137.Google Scholar
Patel, R. P. 1973 An experimental study of a plane mixing layer. AIAA J. 11, 67.Google Scholar
Patnaik, P. C., Corcos, G. M. & Sherman, F. S. 1976 A numerical simulation of Kelvin–Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215.Google Scholar
Peltier, W. R., Halle, J. & Clarke, T. L. 1978 The evolution of finite amplitude Kelvin–Helmholtz billows. Geophys. Astrophys. Fluid Dyn. 10, 53.Google Scholar
Pui, N. K. & Gartshore, I. 1978 Measurements of the growth rate and structure in plane turbulent mixing layers. J. Fluid Mech. 91, 111.Google Scholar
Riley, J. J. & Metcalfe, R. W. 1980 Direct numerical simulation of a perturbed turbulent mixing layer. AIAA Paper 80–0274, AIAA 18th Aerospace Sciences Meeting, Jan. 14–16, Pasadena, California.
Spencer, B. W. & Jones, B. G. 1971 Statistical investigation of pressure and velocity fields in the turbulent two-stream mixing layer. AIAA Paper 71, p. 613.Google Scholar
Thorpe, S. A. 1971 Experiments on the instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46, 299.Google Scholar
Weisbrot, I., Einav, S. & Wygnanski, I. 1982 The nonunique rate of spread of the two-dimensional mixing layer. Phys. Fluids 25, 1691.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanics of turbulent mixing layer growth at moderate Reynolds numbers. J. Fluid Mech. 63, 237.Google Scholar
Wygnanski, I. & Fiedler, H. E. 1970 The two-dimensional mixing region. J. Fluid Mech. 41, 327.Google Scholar