Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-18T18:55:48.807Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional shear layers via vortex dynamics

Published online by Cambridge University Press:  21 April 2006

W. T. Ashurst  and
Eckart Meiburg
W. T. Ashurst
Affiliation:
Sandia National Laboratories, Livermore, CA 94550, USA
Eckart Meiburg
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of the two- and three-dimensional structures in a temporally growing plane shear layer is numerically simulated with the discrete vortex dynamics method. We include two signs of vorticity and thus account for the effect of the weaker boundary layer leaving the splitter plate which is used to create a spatially developing mixing layer. The interaction between the two layers changes the symmetry properties seen in a single vorticity-layer calculation and results in closer agreement with experimental observations of the interface between the two streams. Our calculations show the formation of concentrated streamwise vortices in the braid region between the spanwise rollers, whereas the spanwise core instability is observed to grow only initially. Comparison with flow visualization experiments is given, and we find that the processes dominating the early stages of the mixing-layer development can be understood in terms of essentially inviscid vortex dynamics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 189 , April 1988 , pp. 87 - 116
Copyright
© 1988 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.)

References

Anderson, C. & Greengard, C. 1985 On vortex methods. SIAM J. Numer. Anal. 22, 413.Google Scholar
Aref, H. & Flinchem, E. P. 1984 Dynamics of a vortex filament in a shear flow. J. Fluid Mech. 148, 477–497.Google Scholar
Ashurst, W. T. 1979 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), vol. 1, p. 402. Springer.
Ashurst, W. T. & Meiron, D. I. 1987 Numerical study of vortex reconnection. Phys. Rev. Lett. 58, 1632.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Beale, J. T. 1986 A convergent 3-D vortex method with grid-free stretching. Math. Comp. 46, 401–424.Google Scholar
Bernal, L. P. 1981 The coherent structure of turbulent mixing layers. Part 1. Similarity of the primary vortex structure. Part 2. Secondary streamwise vortex structure. Ph.D. thesis, Graduate Aeronautical Laboratories, California Institute of Technology.
Breidenthal, R. 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.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
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
Greengard, C. 1986 Convergence of the vortex filament method. Math. Comp. 47, 387–398.Google Scholar
Jimenez, J. 1983 A spanwise structure in the plane shear layer. J. Fluid Mech. 132, 319–336.Google Scholar
Jimenez, J., Cogollos, M. & Bernal, L. P. 1985 A perspective view of the plane mixing layer. J. Fluid Mech. 152, 125–143.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, Graduate Aeronautical Laboratories, California Institute of Technology.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lang, D. 1985 Laser Doppler velocity and vorticity measurements in turbulent shear layers. Ph.D. thesis, Graduate Aeronautical Laboratories, California Institute of Technology.
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
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, 53–86.Google Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comp. Phys. 37, 289–335.Google Scholar
Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex elements. Ann. Rev. Fluid Mech. 17, 523–559.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 streamwise vortices. J. Fluid Mech. 141, 139–178.Google Scholar
Meiburg, E. & Lasheras, J. C. 1986 Comparison between experiments and numerical simulations of three-dimensional plane wakes. Phys. Fluids 30, 623–625.Google Scholar
Nakamura, Y., Leonard, A. & Spalart, P. 1982 Vortex simulation of an inviscid shear layer. AIAA paper 82-0948.
Neu, J. C. 1984 The dynamics of stretched vortices. J. Fluid Mech. 143, 253–276.Google Scholar
Pierrehumbert, R. T. 1986 Remarks on a paper by Aref and Flinchem. J. Fluid Mech. 163, 21–26.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. & Orszag, S. A. 1986 Direct numerical simulations of chemically reacting turbulent mixing layers. Phys. Fluids 29, 406–422.Google Scholar
Robinson, A. C. & Saffman, P. G. 1984 Three-dimensional instability of an elliptical vortex in a straining field. J. Fluid Mech. 142, 451–466.Google Scholar
Rogers, R. M. & Moin, P. 1987 The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33–66.Google Scholar
Siggia, E. D. 1985 Collapse and amplification of a vortex filament. Phys. Fluids 28, 794–805.Google Scholar
Tsai, C. Y. & Widnall, S. E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721–733.Google Scholar
Williamson, J. H. 1980 Low-storage Runge-Kutta schemes. J. Comp. Phys. 35, 48–56.Google Scholar
Zabusky, N. J. 1981 Computational synergetics and mathematical innovation. J. Comp. Phys. 43, 195–249.Google Scholar