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Evolution of stream wise vortices and generation of small-scale motion in a plane mixing layer

Published online by Cambridge University Press:  26 April 2006

K. J. Nygaard  and
A. Glezer
K. J. Nygaard
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona. Tucson, AZ 85721, USA
A. Glezer
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona. Tucson, AZ 85721, USA
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Abstract

The evolution of streamwise vortices in a plane mixing layer and their role in the generation of small-scale three-dimensional motion are studied in a closed-return water facility. Spanwise-periodic streamwise vortices are excited by a time-harmonic wavetrain with span wise-periodic amplitude variations synthesized by a mosaic of 32 surface film heaters flush-mounted on the flow partition. For a given excitation frequency, virtually any span wise wavelength synthesizable by the heating mosaic can be excited and can lead to the formation of streamwise vortices before the rollup of the primary vortices is completed. The onset of streamwise vortices is accompanied by significant distortion in the transverse distribution of the streamwise velocity component. The presence of inflexion points, absent in corresponding velocity distributions of the unforced flow, suggests the formation of locally unstable regions of large shear in which broadband perturbations already present in the base flow undergo rapid amplification, followed by breakdown to small-scale motion. Furthermore, as a result of spanwise-non-uniform excitation the cores of the primary vortices are significantly altered. The three-dimensional features of the streamwise vortices and their interaction with the base flow are inferred from surfaces of r.m.s. velocity fluctuations and an approximation to cross-stream vorticity using three-dimensional single component velocity data. The striking enhancement of small-scale motion and the spatial modification of its distribution, both induced by the streamwise vortices, can be related to the onset of the mixing transition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 257 - 301
Copyright
© 1991 Cambridge University Press

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References

Ashurst, W. T. & Meiburg, E. 1988 Three-dimensional shear layers via vortex dynamics. J. Fluid Mech. 189, 87–116.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bell, J. H. & Mehta, R. D. 1989 Three-dimensional structure of plane mixing layers. Joint Institute of Aeronautics and Acoustics Rep. TR-90. NASA Ames Research Center.Google Scholar
Bernal, L. P. 1981 The coherent structure of turbulent mixing layers. I. Similarity of the primary vortex structure. II. Secondary streamwise vortex structure. Ph.D. thesis, California Institute of Technology.
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Breidenthal, R. E. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.Google Scholar
Browand, F. K. & Troutt, T. R. 1980 A note on span wise 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 larger 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
Buell, J. C. & Mansour, N. N. 1989 Asymmetric effects in three-dimensional spatially developing mixing layers. In Proc. Seventh Symp. on Turbulent Shear Flows, Stanford University, pp. 9.2.1–9.2.6.
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, G7–108.Google Scholar
Chandrsuda, C., Mehta, R. D., Weir, A. D. & Bradshaw, P. 1978 Effect of free-stream turbulence on large structures in turbulent mixing layers. J. Fluid Mech. 85, 693–704.Google Scholar
Corcos, G. M. 1988 The role of cartoons in turbulence. In Perspectives in Fluid Mechanics (ed. D. E. Coles). Lecture Notes in Physics, vol. 320, pp. 48–65. Springer.
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, 67–95.Google Scholar
Fiedler, H. E. 1988 Coherent structures in turbulent flows. Prog. Aerospace Sci. 25, 231–269.Google Scholar
Fiedler, H. E., Glezer, A. & Wygnanski, I. J. 1988 Control of the plane mixing layer: some novel experiments. In Current Trends in Turbulence Research (ed. H. Branover, M. Mond & Y. Unger), vol. 112, pp. 30–64.
Fiedler, H. E., Nottmeyer, K., Wegener, P. P. & Raghu, S. 1985 Schlieren photography of water flow. Exps Fluids 3, 145–151.Google Scholar
Gaster, M., Kit, E. & Wygnanski, I. J. 1985 Large scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–47.Google Scholar
Glezer, A. & Coles, D. E. 1990 An experimental investigation of a turbulent vortex ring. J. Fluid Mech. 211, 243–283.Google Scholar
Glezer, A., Katz, Y. & Wygnanski, I. J. 1989 On the breakdown of the wave packet trailing a turbulent spot in a laminar boundary layer. J. Fluid Mech. 198, 1–26.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Huang, L.-S. & Ho, C.-M. 1990 Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475–500.Google Scholar
Hussain, A. K. M. F. 1983 Coherent structures and incoherent turbulence. In Turbulence and Chaotic Phenomena in Fluids: Proc. Intl Symp. on Turbulence and Chaotic Phenomena in Fluids, Kyoto, Japan (ed. T. Tatsumi). Elsevier.
Jimenez, J. 1983 A spanwise structure in the plane shear layer. J. Fluid Mech. 132, 319–336.Google Scholar
Jimenez, J., Martinez-Val, R. & Rebollo, M. 1979 On the origin and evolution of three-dimensional effects in the mixing layer. Final Rep. DA-ERO 79-G-079. Universidad Politecnica de Madrid. AD-A096007.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary layer instability. J. Fluid Mech. 12, 1–41.Google Scholar
Konrad, J. H. 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion limited chemical reactions. Ph.D. thesis. California Institute of Technology.
Landahl, M. T. & Mollo-Christensen, E. 1986 Turbulence and Random Processes in Fluid Mechanics. Cambridge University Press.
Lasheras, J. S. & Choi, H. 1088 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53–86.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, 231–258.Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Ann. Rev. Fluid Mech. 15, 391–427.Google Scholar
Liepmann, H. W., Brown, G. L. & Nosenchuck, D. M. 1982 Control of laminar instability-waves using a new technique. J. Fluid Mech. 118, 187–200.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic model of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.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, 207–243.Google Scholar
Miksad, R. W. 1972 Experiments on the nonlinear stages of free-shear-layer transition. J. Fluid Mech. 56, 695–719.Google Scholar
Nygaard, K. J. 1987 Construction, instrumentation, and testing of a span wise forced plane mixing layer facility. M.S. Report. The University of Arizona.
Nygaard, K. J. & Glezer, A. 1989 On the spanwise structure of a plane mixing layer. In Advances in Turbulence 2 (ed. H.-H. Fernholtz & H. E. Fiedler), pp. 461–466. Springer.
Nygaard, K. J. & Glezer, A. 1990 Core instability of the spanwise vortices in a plane mixing layer. Phys. Fluids A 2, 461–464.Google Scholar
Nygaard, K. J. & Glezer, A. 1991 Phase excitation of a plane mixing layer. J. Fluid Mech. (to be submitted).Google Scholar
Oster, D. & Wygnanski, I. 1982 The forced mixing layer between parallel stream. J. Fluid Mech. 123, 91–130.Google Scholar
Pierrehumbert, R. T. 1986 Universal short-wave instability of two-dimensional eddies in an inviscid fluid. Phys. Rev. Lett. 57, 2157–2159.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
Pullin, D. I. & Jacobs, P. A. 1986 Inviscid evolution of stretched vortex arrays. J. Fluid Mech. 171, 377–406.Google Scholar
Riley, J. J., Mourad, P. D., Moser, R. D. & Rogers, M. M. 1988 Sensitivity of mixing layers to three-dimensional forcing. In Center for Turbulence Research: Proc. Summer Program 1988, pp. 91–116. Center for Turbulence Research.
Roberts, F. A. 1985 Effects of a periodic disturbance on structure and mixing in turbulent shear layers and wakes. Ph.D. thesis, California Institute of Technology.
Rogers, M. M. & Moser, R. D. 1989 The development of three-dimensional temporally evolving mixing layers. In Proc. Seventh Symp. on Turbulent Shear Flows, Stanford University, pp. 9.3.1.-9.3.6.
Roshko, A. 1981 The plane mixing layer; flow visualization results and three-dimensional effects. In The Role of Coherent Structures in Modelling Turbulence and Mixing (ed. J. Jimenez). Lecture Notes in Physics, vol. 136, pp. 208–217. Springer.
Saric, W. S. & Thomas, A. S. W. 1983 Experiments on the subharmonic routes to turbulence in boundary layers. In Turbulence and Chaotic Phenomena in Fluids: Proc. Intl Symp. on Turbulence and Chaotic Phenomena in Fluids, Kyoto, Japan (ed. T. Tatsumi). Elsevier.
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Townsend, A. A, 1980 The Structure of Turbulent Shear Flows, 2nd edn. Cambridge University Press.
Weisbrot, I. 1984 A highly excited turbulent mixing layer. M.S. thesis Tel Aviv University.