Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-26T22:20:54.646Z Has data issue: false hasContentIssue false
  • English
  • Français

On solutions relating to conical vortices over a plane wall

Published online by Cambridge University Press:  26 April 2006

C. Sozou
C. Sozou
Affiliation:
Department of Applied and Computational Mathematics, The University, Sheffield S10 2TN, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that certain similarity solutions relating to axisymmetric vortices in a viscous fluid over a plane wall can be associated with a point source or sink of vorticity at the origin and a line vortex along the symmetry axis of the system. The rotationality of the nonlinear terms in the momentum equation, due to the radial vorticity and the azimuthal flow field, induces a poloidal flow which relates to one-cell or two-cell configurations. It is shown that a small imput of radial vorticity into a strong line vortex can induce an intense up-draught. There are ranges of values of the parameters yielding two solutions. The extremeties of these ranges are associated with values that yield velocity breakdown.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 633 - 644
Copyright
© 1992 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.)

Footnotes

With an Appendix by M. A. Goldshtik and V. N. Shtern

References

Goldshtik M. A. 1960 J. Appl. Math. Mech. 24, 913–929.
Goldshtik, M. A. & Shtern V. N. 1990 J. Fluid Mech. 218, 483–508.
Lighthill M. J. 1963 In Laminar Boundary Layers (ed. L. Rosenhead), p. 50. Oxford University Press.
Lundquist S. 1969 Ark. Fys. 40, 89–95.
Maxworthy T. 1973 J. Atmos. Sci. 30, 1717–1722.
Paull, R. & Pillow A. F. 1985a J. Fluid Mech. 155, 343–358.
Paull, R. & Pillow A. F. 1985b J. Fluid Mech. 155, 359–379.
Serrin J. 1972 Phil Trans. R. Soc. Lond. A 271, 325–360.
Shivola, E. I. & Shcherbinin E. 1971 Magnetohydrodyn. 7, 167–171 (English transl.).
Simpson J. 1982 In Intense atmospheric vortices (ed. L. Bengtsson & J. Lighthill), pp. 161–173. Springer.
Simpson J., Morton B. R., McCumber, M. C. & Penc R. S. 1986 J. Atmos. Sci. 43, 753–782.
Snow J. T. 1984 Sci. Am. 250 (4), 56–66.
Sozou C. 1971 J. Fluid Mech. 46, 25–32.
Sozou, C. & English H. 1972 Proc. R. Soc. Lond. A 329, 71–82.
Squire H. B. 1952 Phil. Mag. 43 (7), 942–945.
Yih C. S., Wu F., Garg, A. K. & Leibovich S. 1982 Phys. Fluids 25, 2147–2158.