Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-02T02:01:15.779Z Has data issue: false hasContentIssue false
  • English
  • Français

Merger and cancellation of strained vortices

Published online by Cambridge University Press:  26 April 2006

James D. Buntine  and
D. I. Pullin
James D. Buntine
Affiliation:
Department of Mechanical Engineering, University of Queensland, St Lucia, 4067 Queensland, Australia Present address: Applied Mathematics 217–50, California Institute of Technology, Pasadena, CA 91125, USA.
D. I. Pullin
Affiliation:
Department of Mechanical Engineering, University of Queensland, St Lucia, 4067 Queensland, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

We study numerically the behaviour of and interaction between Burgers vortices – a known equilibrium solution to the Navier–Stokes equations which incorporates a balance between viscous diffusion and strain intensification of vorticity. A hybrid spectral/finite-difference method is employed to solve the Navier–Stokes equations in vorticity–stream function form for a unidirectional vorticity field on an infinite domain in the presence of a uniform three-dimensional strain field, one principal axis of which is parallel to the vorticity. Merging of two strained vortices is studied over a range of Reynolds numbers Re = Γ/2πν = 10–1280, and the results are used to calculate an energy spectrum for three-dimensional, homogeneous turbulence. The cancellation of two strained vortices with opposing circulation is investigated for Reynolds numbers Re = Γ0/2πν = 0.1–160 (τ0 is the circulation about one vortex), over a range of strain rates in the direction parallel to the line joining the vortex centres. A solution of the Navier–Stokes equations describing vorticity cancellation in the strain-induced collision of vortex layers (Kambe 1984) is used to estimate the asymptotic, timewise decay of circulation for each vortex. Good agreement with the present numerical results is obtained. Vortex core pressures calculated during the cancellation event are compared to a simple analytical model based on Moore & Saffman (1971).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 205 , August 1989 , pp. 263 - 295
Copyright
© 1989 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

Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 2343–2353.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171–199.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, 67–96.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, 29–65.Google Scholar
Deem, G. S. & Zabusky, N. J. 1978 Stationary V-states: interactions, recurrence and breaking. Phys. Rev. Lett. 40, 859.Google Scholar
Giga, Y. & Kambe, T. 1987 Large time behaviour of the vorticity of two dimensional viscous flow and vortex formation in three-dimensional flow. IUTAM Symp. on Fundamental Aspects of Vortex Motion, Tokyo, Japan.
Hinze, J. O. 1975 Turbulence, 2nd edn. McGraw-Hill.
Jacobs, P. A. 1987 Nonlinear dynamics of piecewise-constant vorticity distributions in an inviscid fluid. Ph.D. Thesis, University of Queensland.
Jacobs, P. A. & Pullin, D. I. 1985 Coalescence of stretching vortices. Phys. Fluids 28, 1619–1625.Google Scholar
Kambe, T. 1984 Some dissipation mechanisms in vortex systems. In Turbulence and Chaotic Phenomena, (ed. T. Tatsumo), pp. 239–244. IUTAM.
Kida, S. 1981 Motion of an elliptic vortex in a uniform shear flow. J. Phys. Soc. Japan 50, 3157.Google Scholar
Leonard, A. & Wincklemans, G. 1988 Improved vortex methods for three-dimensional flows with applications to the interactions of two vortex rings. SIAM Workshop on Mathematical Aspects of Vortex Dynamics, Leesburg Virginia, April 25–28.
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.CrossRefGoogle Scholar
Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–2203.Google Scholar
Meiron, D. I., Orszag, S. A. & Shelly, M. J. 1988 A numerical study of vortex reconnection. SIAM Workshop on Mathematical Aspects of Vortex Dynamics, Leesburg, Virginia, April 25–28.
Melander, M. V., McWilliams, J. C. & Zabusky, N. J. 1987 Axisymmetrization and vorticitygradient intensification of an isolated two-dimensional vortex through filamentation. J. Fluid Mech. 178, 137–159.Google Scholar
Melander, M. V., Zabusky, N. J. & McWilliams, J. C. 1988 Symmetric vortex merger in two dimensions: causes and conditions. J. Fluid Mech. 195, 303–340.Google Scholar
Moore, D. W. & Saffman, P. G. 1971 Structure of a line vortex in an imposed strain. In Aircraft J Wake Turbulence (ed. J. Olsen, A. Goldberg & N. Rogers), pp. 339–354. Plenum.
Neu, J. C. 1984a The dynamics of a columnar vortex in an imposed strain. Phys. Fluids 27, 2397–2402.Google Scholar
Neu, J. C. 1984b The dynamics of stretched vortices. J. Fluid Mech. 143, 253–276.Google Scholar
Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129, 409–426.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–218.Google Scholar
Robinson, A. C. & Saffman, P. G. 1984 Stability and structure of stretched vortices. Stud. Appl. Maths 70, 163–181.Google Scholar
Schatzle, P. R. 1987 An experimental study of fusion of vortex rings. Ph.D. Thesis, California Institute of Technology.
Siggia, E. D. & Pumir, A. 1988 Incipient singularities in the Navier-Stokes equations. Preprint Cornel University.
Townsend, A. A. 1951 On the fine-scale structure of turbulence. Proc. R. Soc. Lond. A 208, 534–542.Google Scholar