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The motion of a cylinder of fluid released from rest in a cross-flow

Published online by Cambridge University Press:  21 April 2006

James W. Rottman ,
John E. Simpson  and
Peter K. Stansby
James W. Rottman
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Present address: Department of Marine, Earth & Atmospheric Sciences, North Carolina State University, Raleigh, NC 27695, USA.
John E. Simpson
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
Peter K. Stansby
Affiliation:
Department of Engineering, Simon Engineering Laboratories, University of Manchester, Oxford Road, Manchester M13 9PL, UK
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Abstract

The two-dimensional motion of a cylinder of fluid released from rest into a flow that is uniform far upstream of the cylinder is studied. We consider cases where the cylinder is initially of circular cross-section and the fluid is either inviscid or viscous. For the inviscid fluid, we use analytical methods to determine the motion for small and large times after release and three numerical methods, the vortex-sheet method, the vortex-blob method and the vortex-in-cell method, to determine the intermediate-time motion. For the viscous-fluid problem we use the vortex-in-cell method with random walks to compute both the initial flow around the cylinder and the motion of the released fluid at a Reynolds number of 484. In the inviscid case, the released fluid deforms into a structure that resembles a vortex pair that propagates down stream at a speed less than the onset flow speed. In the viscous case, after a wake representative of a Kármán vortex street has developed, the released fluid usually deforms into an elongated horseshoe shape that travels downstream at a speed greater or less than the incident flow speed (depending on when in the vortex-shedding cycle the cylinder is released). The results of the numerical calculations are compared with some simple experiments in a water channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 307 - 337
Copyright
© 1987 Cambridge University Press

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References

Baker, G. R. 1979 The cloud-in-cell technique applied to the roll-up of vortex sheets. J. Comp. Phys. 31, 76–95.Google Scholar
Baker, G. R. 1980 A test of the method of Fink and Soh for following vortex-sheet motion. J. Fluid Mech. 100, 209–220.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Britter, R. E. & Simpson, J. E. 1978 Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88, 223–240.Google Scholar
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 785–796.Google Scholar
Chorin, A. J. 1978 Vortex sheet approximation of boundary layers. J. Comp. Phys. 27, 428–442.Google Scholar
Chorin, A. J. & Bernard, P. S. 1973 Discretisation of a vortex sheet with an example of roll-up. J. Comp. Phys. 13, 423–429.Google Scholar
Christiansen, J. P. 1973 Numerical simulation of hydrodynamics by a method of point vortices. J. Comp. Phys. 13, 363–379.Google Scholar
Fink, P. T. & Soh, W. K. 1978 A new approach to roll-up calculations of vortex sheets. Proc. R. Soc. Lond. A 362, 195–209.Google Scholar
Hald, O. 1979 The convergence of vortex methods II. SIAM J. Numer. Anal. 16, 726–755.Google Scholar
Hall, D. J., Hollis, E. J. & Ishaq, H. 1984 A wind tunnel model of the Porton dense gas spill field trials. In Proc. IUTAM Symp. on Atmospheric Dispersion of Heavy Gases and Small Particles, Delft, The Netherlands, August 1983 (ed. G. Ooms & H. Tennekes). Springer.
Krasny, R. 1986a A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167, 65–93.Google Scholar
Krasny, R. 1986b Desingularization of periodic vortex sheet roll-up. J. Comp. Phys. 65, 292–313.Google Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comp. Phys. 37, 289–335.Google Scholar
Mcquaid, J. 1984 Large scale experiments on the dispersion of heavy gas clouds. In Proc. IUTAM Symp. on Atmospheric Dispersion of Heavy Gases and Small Particles, Delft, The Netherlands, August 1983 (ed. G. Ooms & H. Tennekes). Springer.
Meiron, D. I., Baker, G. R. & Orszag, S. A. 1982 Analytic structure of vortex sheet dynamics. Part I. Kelvin-Helmholtz instability. J. Fluid Mech. 114, 283–298.Google Scholar
Moore, D. W. 1979 The spontaneous appearance of a singularity in the shape of an evolving vortex sheet. Proc. R. Soc. Lond. A 365, 105–119.Google Scholar
Moore, D. W. 1981 On the point vortex method. SIAM J. Sci. Stat. Comput. 2, 65–84.Google Scholar
Picknett, R. G. 1981 Dispersion of dense gas puffs released in the atmosphere at ground level. Atmos. Environ. 15, 509–525.Google Scholar
Pierrehumbert, R. T. 1980 A family of steady, translating vortex pairs with distributed vorticity. J. Fluid Mech. 99, 129–144.Google Scholar
Roberts, A. J. 1983 A stable and accurate numerical method to calculate the motion of a sharp interface between fluids. IMA J. Appl. Maths. 31, 13–35.Google Scholar
Saffman, P. G. & Baker, G. R. 1979 Vortex interactions. Ann. Rev. Fluid Mech. 11, 95–112.Google Scholar
Schwartz, L. W. 1981 A semi-analytic approach to self-induced motion of vortex sheets. J. Fluid Mech. 111, 475–490.Google Scholar
Smith, P. A. 1986 Computation of viscous flows by the vortex method. PhD thesis, University of Manchester.
Smith, P. A. & Stansby, P. K. 1985 Wave-induced bed flows by a Lagrangian vortex scheme. J. Comp. Phys. 60, 489–516.Google Scholar
Stansby, P. K. & Dixon, A. G. 1983 Simulation of flows around cylinders by a Lagrangian vortex scheme. Appl. Ocean. Res. 5, 167–178.Google Scholar
Taylor, G. I. 1953 Formation of a vortex ring by giving an impulse to a circular disc and the dissolving it away. J. Appl. Phys. 24, 104–105.Google Scholar
Thom, A. 1928 An investigation of fluid flow in two dimensions. Aero. Res. Counc. R & M, No. 1194, 166–183.Google Scholar