Skip to main content
SpringerLink
Log in

Computation of vortex sheet roll-up

  • Vortex Sheets
  • Conference paper
  • First Online:
Vortex Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1360))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, C. R. 1985 A vortex method for flows with slight density variations. J. Comp. Phys. 61, 417.

    Article  MathSciNet  MATH  Google Scholar 

  2. Baker, G. R. 1979 The “Cloud in Cell” technique applied to the roll-up of vortex sheets. J. Comp. Phys. 31, 76.

    Article  MathSciNet  MATH  Google Scholar 

  3. Baker, G. R. & Shelley, M. 1987 these preceedings.

    Google Scholar 

  4. Birkhoff, G. 1962 Helmholtz and Taylor instability. Proc. Symp. Appl. Math. XIII A.M.S., 55.

    Google Scholar 

  5. Caflisch, R. & Orellana, O. 1986 Long time existence for a slightly perturbed vortex sheet. Comm. Pure Appl. Math. 39, no. 6, 807.

    Article  MathSciNet  MATH  Google Scholar 

  6. Chorin, A. J. & Bernard, P. S. 1973 Discretization of a vortex sheet, with an example of roll-up. J. Comp. Phys. 13, 423.

    Article  MATH  Google Scholar 

  7. DiPerna, R. J. & Majda, A. 1987 Concentrations in regularizations for 2-D incompressible flow. Comm. Pure Appl. Math. 40, no. 3, 301.

    Article  MathSciNet  MATH  Google Scholar 

  8. Hoeijmakers, H. W. M. & Vaatstra, W. 1983 A higher-order panel method applied to vortex sheet roll-up. AIAA J. 21, 516.

    Article  MATH  Google Scholar 

  9. Krasny, R. 1986 A study of singularity formation in a vortex sheet by the point vortex approximation. J. Fluid Mech. 167, 65.

    Article  MathSciNet  MATH  Google Scholar 

  10. Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comp. Phys. 65, 292.

    Article  MATH  Google Scholar 

  11. Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123.

    Article  Google Scholar 

  12. Lax, P. D. 1973 Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Reg. Conf. Ser. Appl. Math. SIAM 11.

    Google Scholar 

  13. Meiron, D. I., Baker, G. R. & Orszag, S. A. 1982 Analytic structure of vortex sheet dynamics. I. Kelvin-Helmholtz instability. J. Fluid Mech. 114, 283.

    Article  MathSciNet  MATH  Google Scholar 

  14. Moore, D. W. 1974 A numerical study of the roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225.

    Article  MATH  Google Scholar 

  15. Moore, D. W. 1976 The stability of an evolving two-dimensional vortex sheet. Matematika 23, 35.

    Article  MathSciNet  MATH  Google Scholar 

  16. 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.

    Article  MathSciNet  MATH  Google Scholar 

  17. Moore, D. W. 1981 On the point vortex method. SIAM J. Sci. Stat. Comput. 2, 65.

    Article  MathSciNet  MATH  Google Scholar 

  18. Pullin, D. I. 1982 Numerical studies of surface-tension effects in nonlinear Kelvin-Helmholtz instability and Rayleigh-Taylor instability. J. Fluid Mech. 119, 507.

    Article  MathSciNet  MATH  Google Scholar 

  19. Rosenhead, L. 1931 The formation of vortices from a surface of discontinuity. Proc. R. Soc. Lond. A 134, 170.

    Article  MATH  Google Scholar 

  20. Saffman, P. G. & Baker, G. R. 1979 Vortex interactions. Ann. Rev. Fluid Mech. 11, 95.

    Article  MATH  Google Scholar 

  21. Sulem, C., Sulem, P. L., Bardos, C. & Frisch, U. 1981 Finite time analyticity for the two and three dimensional Kelvin-Helmholtz instability. Comm. Math. Phys. 80, 485.

    Article  MathSciNet  MATH  Google Scholar 

  22. Tryggvasson, G. 1987 Simulation of vortex sheet roll-up by vortex methods. J. Comp. Phys. to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of Michigan, 48109, Ann Arbor, Michigan

    Robert Krasny

Authors
  1. Robert Krasny
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Christopher Anderson Claude Greengard

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Krasny, R. (1988). Computation of vortex sheet roll-up. In: Anderson, C., Greengard, C. (eds) Vortex Methods. Lecture Notes in Mathematics, vol 1360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089767

Download citation

  • DOI: https://doi.org/10.1007/BFb0089767

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50526-6

  • Online ISBN: 978-3-540-46034-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation