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Inviscid evolution of stretched vortex arrays

Published online by Cambridge University Press:  21 April 2006

D. I. Pullin  and
P. A. Jacobs
D. I. Pullin
Affiliation:
Department of Mechanical Engineering, University of Queensland, St Lucia, 4067, Australia
P. A. Jacobs
Affiliation:
Department of Mechanical Engineering, University of Queensland, St Lucia, 4067, Australia
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Abstract

The nonlinear evolution of an array of pairs of inviscid counter-rotating vortices, subjected to an applied stretching strain field, has been studied numerically using the contour-dynamics method. The array configuration is effectively the Corcos-Lin model of streamwise vortices in the braid region of a nominally two-dimensional mixing layer. For each individual vortex the simulations elucidate the strong interaction between the vortex self-induction, the vorticity amplification of the stretching strain, and the local in-plane strain applied by all other members of the array. When the initial vorticity distribution is modelled by a non-uniform piece-wise-constant vorticity field defined over a nested set of non-intersecting contours, the dynamical evolution reveals fine structure consisting of strong vortex roll-up accompanied by trailing, filament-like spiral vortex sheets, and the presence of tertiary instabilities. It is shown by a particular example that these features are largely absent in an equivalent computation in which array members are modelled by the commonly used uniform-vortex approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 377 - 406
Copyright
© 1986 Cambridge University Press

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References

Bernal L. P.1981 The coherent structure of turbulent mixing layers. II. Secondary streamwise vortex structure. Ph.D. thesis, 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
Burgers J. M.1948 A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171–196.Google Scholar
Corcos, G. M. & Lin S. J.1984 The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of three-dimensional motion. J. Fluid Mech. 139, 67–95.Google Scholar
Corcos, G. M. & Sherman F. S.1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and two-dimensional flow. J. Fluid Mech. 139, 29–65.Google Scholar
Couët, B. & Leonard A.1980 Mixing layer simulation by an improved three-dimensional vortex-in-cell algorithm. Proc. 7th Intl Conf. on Numerical Methods in Fluid Dynamics. Stanford, Ames.
Jacobs, P. A. & Pullin D. I.1985 Coalescence of stretching vortices. Phys. Fluids. 28, 1619–1625.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
Kaden H.1931 Aufwicklung einer unstabilen Unstetigkeitsflache. Ing. Arch. 2, 140. (English trans. R.A. Lib. Trans. no. 403.)Google Scholar
Lamb H.1932 Hydrodynamics, 6th edn. Cambridge University Press.
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
Lundgren T. S.1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids. 25, 2193–2203.Google Scholar
Meiron D. I., Baker, G. R. & Orszag S. A.1982 Analytic structure of vortex sheet dynamics. Part 1. Kelvin-Helmholtz instability. J. Fluid Mech. 114, 283–298.Google Scholar
Meiron D. I., Saffman, P. G. & Schatzman J. C.1984 The linear two-dimensional stability of inviscid vortex streets of finite-cored vortices. J. Fluid Mech. 147, 187–212.Google Scholar
Moore, D. W. & Saffman P. G.1973 Axial flow in laminar trailing vortices Proc. R. Soc. Lond. A 333, 491–508.Google Scholar
Neu J.1984a The dynamics of a columnar vortex in an imposed strain Phys. Fluids, 27, 2397.Google Scholar
Neu J.1984b The dynamics of stretched vortices. J. Fluid Mech. 143, 253–276.Google Scholar
Overman, E. A. & Zabusky N. J.1982 Evolution and merger of isolated vortex structures Phys. Fluids, 25, 1297–1305.Google Scholar
Pierrehumbert, R. T. & Widnall S. E.1982 The two-and-three dimensional instabilities of a spacially periodic shear layer. J. Fluid Mech. 114, 59–82.Google Scholar
Pullin D. I.1981 The nonlinear behaviour of a constant vorticity layer at a wall. J. Fluid Mech. 108, 401.Google Scholar
Pullin, D. I. & Phillips W. R. C.1981 On a generalization of Kaden's problem. J. Fluid Mech. 104, 45–53.Google Scholar
Robinson, A. C. & Saffman P. G.1984 Stability and structure of stretched vortices. Stud. Appl. Maths. 10, 163–181.Google Scholar
Roshko A.1980 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.
Zabusky N. J., Hughes, M. H. & Roberts K. V.1979 Contour Dynamics for the Euler equations in two dimensions. J. Comp. Phys. 30, 96–106.Google Scholar