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Exact vortex solutions of the Navier–Stokes equations with axisymmetric strain and suction or injection

Published online by Cambridge University Press:  10 May 2009

ALEX D. D. CRAIK
ALEX D. D. CRAIK*
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews, Fife KY16 9SS, Scotland, UK
*
†Email address for correspondence: [email protected]
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Abstract

New solutions of the Navier–Stokes equations are presented for axisymmetric vortex flows subject to strain and to suction or injection. Those expressible in simple separable or similarity form are emphasized. These exhibit the competing roles of diffusion, advection and vortex stretching.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 291 - 306
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. (Eds) 1965 Handbook of Mathematical Functions. Dover.Google Scholar
Bateman, H. 1923 The decay of a simple eddy: Report No. 144. 8th Annual Report of NACA for 1922, pp. 317–323.Google Scholar
Bateman, H. 1932 Partial Differential Equations of Mathematical Physics. Cambridge University Press (also reprinted by Dover, 1944).Google Scholar
Burgers, J. M. 1948 Adv. Appl. Mech. 1, 171–199.CrossRefGoogle Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd ed.Clarendon Press.Google Scholar
Drazin, P. G. & Riley, N. 2006 The Navier–Stokes Equations: A Classification of Flows and Exact Solutions. Cambridge University Press.CrossRefGoogle Scholar
Dritschel, D. G., Tran, C. V. & Scott, R. K. 2007 J. Fluid Mech. 591, 379–391.CrossRefGoogle Scholar
Fukumoto, Y. 1990 J. Phys. Soc. Jpn 59, 918–926.CrossRefGoogle Scholar
Gibbon, J. D., Fokas, A. S., & Doering, C. R. 1999 Physica D 132, 497–510.CrossRefGoogle Scholar
Kambe, T. 1983 J. Phys. Soc. Jpn 52, 834.CrossRefGoogle Scholar
Kambe, T. 1984 a J. Phys. Soc. Jpn 53, 13–15.CrossRefGoogle Scholar
Kambe, T. 1984 b Proc. IUTAM Symp. Turbulence and chaotic phenomena in fluids. (Kyoto, 1983) (ed. Tatsumi, T.). North Holland, Amsterdam.Google Scholar
Kamke, E. 1959 Differentialgleichungen Lösungsmethoden und Lösungen Bd.1. Chelsea.Google Scholar
Kerr, R. M. 2005 Phys. Fluids 17, 075103.CrossRefGoogle Scholar
Lundgren, T. S. 1982 Phys. Fluids 25, 2193–2211.CrossRefGoogle Scholar
Moffatt, H. K. 2000 J. Fluid Mech. 409, 51–68.CrossRefGoogle Scholar
Oseen, C. W. 1911 Ark. Mat. Astron. Fys. 7, 14–26.Google Scholar
Rott, N. 1958 Z. Angew. Math. Phys. 9, 543–553.CrossRefGoogle Scholar
Sullivan, R. D. 1959 J. Aerosp. Sci. 26, 767–768.CrossRefGoogle Scholar
Uhlenbeck, G. E. & Ornstein, L. S. 1930 Phys. Rev. 36, 823–841.CrossRefGoogle Scholar