Skip to main content
SpringerLink
Log in

Transport of Vortex Elements

  • Chapter
  • First Online:
Mathematical Modeling of Unsteady Inviscid Flows

Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 50))

  • 958 Accesses

Abstract

Thus far in this book, we have focused our attention on two principal aspects of inviscid flow: first, on obtaining the flow field about a moving body amidst a general distribution of vorticity in the surrounding fluid; and second, on computing the resulting fluid dynamic force and moment exerted on the body in this scenario. We have thus far had little to say about the motion of this vorticity. However, our analysis of the problem is incomplete until we have addressed this motion, particularly because—as we found in our discussion of impulse-based calculations in Chap. 6—the force and moment depend on the time rate of change of the vorticity’s distribution.

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 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    Except at the corners of bodies, where we often will regularize the flow comprehensively according to the Kutta condition.

References

  1. J.T. Beale, A. Majda, High order accurate vortex methods with explicit velocity kernels. J. Comput. Phys. 58, 188–208 (1985)

    Article  Google Scholar 

  2. G. Birkhoff, Helmholtz and Taylor instability, in Hydrodynamic Instability, ed. by G. Birkhoff, R. Bellman, C.C. Lin. Proceedings of Symposia in Applied Mathematics, vol. 13 (1962), pp. 63–84

    Google Scholar 

  3. C.E. Brown, W.H. Michael, Effect of leading edge separation on the lift of a delta wing. J. Aero. Sci. 21, 690–694 (1954)

    Article  Google Scholar 

  4. A.J. Chorin, Numerical study of slightly viscous flow. J. Fluid Mech. 57(4), 785–796 (1973)

    Article  MathSciNet  Google Scholar 

  5. S.C. Crow, Stability theory for a pair of trailing vortices. AIAA J. 8(12), 2172–2179 (1970)

    Article  Google Scholar 

  6. D. Darakananda, J.D. Eldredge, A versatile taxonomy of low-dimensional vortex models for unsteady aerodynamics. J. Fluid Mech. 858, 917–948 (2019). https://doi.org/10.1017/jfm.2018.792

    Article  MathSciNet  Google Scholar 

  7. R.H. Edwards, Leading edge separation from delta wings. J. Aero. Sci. 21, 134–135 (1954)

    Google Scholar 

  8. C. Greengard, The core spreading vortex method approximates the wrong equation. J. Comput. Phys. 61, 345–348 (1985)

    Article  MathSciNet  Google Scholar 

  9. F.R. Hama, Progressive deformation of a curved vortex filament by its own induction. Phys. Fluids 5(10), 1156–1162 (1962)

    Article  Google Scholar 

  10. G. Kirchhoff, Vorlesungen Über Mathematische Physik (Teubner, Leipzig, 1876)

    MATH  Google Scholar 

  11. R. Krasny, Vortex Sheet Computations: Roll-Up, Wake, Separation. Lectures in Applied Mathematics, vol. 28 (AMS, New York, 1991), pp. 385–402

    Google Scholar 

  12. A. Leonard, Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17, 523–559 (1985)

    Article  Google Scholar 

  13. S. Michelin, S.G. Llewelyn Smith, An unsteady point vortex method for coupled fluid–solid problems. Theor. Comput. Fluid Dyn. 23, 127–153 (2009)

    Article  Google Scholar 

  14. D.W. Moore, P.G. Saffman, The motion of a vortex filament with axial flow. Philos. Trans. R. Soc. Lond. A 272(1226), 403–429 (1972)

    Article  Google Scholar 

  15. L.F. Rossi, Resurrecting core spreading vortex methods: a new scheme that is both deterministic and convergent. SIAM J. Sci. Comput. 17(2), 370–397 (1996)

    Article  MathSciNet  Google Scholar 

  16. N. Rott, Diffraction of a weak shock with vortex generation. J. Fluid Mech. 1(1), 111–128 (1956)

    Article  MathSciNet  Google Scholar 

  17. C. Wang, J.D. Eldredge, Low-order phenomenological modeling of leading-edge vortex formation. Theor. Comput. Fluid Dyn. 27(5), 577–598 (2013). https://doi.org/10.1007/s00162-012-0279-5

    Article  Google Scholar 

  18. S.E. Widnall, D. Bliss, A. Zalay, Theoretical and experimental study of the stability of a vortex pair, in Aircraft Wake Turbulence and Its Detection, ed. by J. Olsen, A. Goldburg, M. Rogers (Plenum, New York, 1971), pp. 305–338

    Chapter  Google Scholar 

  19. G.S. Winckelmans, A. Leonard, Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows. J. Comput. Phys. 109(2), 247–273 (1993)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA, USA

    Jeff D. Eldredge

Authors
  1. Jeff D. Eldredge
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Eldredge, J.D. (2019). Transport of Vortex Elements. In: Mathematical Modeling of Unsteady Inviscid Flows. Interdisciplinary Applied Mathematics, vol 50. Springer, Cham. https://doi.org/10.1007/978-3-030-18319-6_7

Download citation

Publish with us

Policies and ethics

Search

Navigation