• Michael S. Broadhurst
  • Vassilios Theofilis
  • Spencer J. Sherwin
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 78)


The scope of the present study is to demonstrate the use of spectral/hp-element methods in understanding the global instability mechanisms of vortex dominated flows. Using a BiGlobal stability analysis, analytically constructed and numerically evaluated base flows have been investigated, with the leading eigenvalues obtained by the Arnoldi algorithm. Subsequently, Direct Numerical Simulation (DNS) was used to investigate the non-linear development of an unstable Batchelor vortex. It was found that a spiral-type instability, if allowed to develop in an axially unconstrained manner, leads to an axial loss of energy and the formation of a stagnation point.


Direct Numerical Simulation Stagnation Point Vortex Breakdown Spectral Element Method Vortical Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abid, M. and Brachet, M.E. (1998). Direct numerical simulations of the Batchelor trailing vortex by a spectral element method. Physics of Fluids, 10(2).Google Scholar
  2. Ash, R.L. and Khorrami, M.R. (1995). Vortex stability. In Green, S.I., editor, Fluid Vortices, pages 317–372. Kluwer Academic Publishers.Google Scholar
  3. Barkley, D. and Tuckerman, L.S. (2000). Bifurcation analysis for timesteppers. In Doedel, E. and Tuckerman, L.S., editors, Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, pages 466–543. Springer, New York.Google Scholar
  4. Batchelor, G.K. (1964). Axial flow in trailing line vortices. Journal of Fluid Mechanics, 20:645-658.zbMATHMathSciNetGoogle Scholar
  5. Benjamin, T.B. (1962). Theory of the vortex breakdown phenomenon. Journal of Fluid Mechanics, 14(4):593–629.MathSciNetGoogle Scholar
  6. Crouch, J.D., Garbaruk, A., Shur, M., and Strelets, M. (2004). Predicting unsteady buffet onset using RANS solutions. TM 2004–212913, NASA.Google Scholar
  7. Herbert, T. (1997). Parabolized stability equations. Annual Review of Fluid Mechanics, 29:245–283.CrossRefMathSciNetGoogle Scholar
  8. Leibovich, S. (1978). The structure of vortex breakdown. Annual Reiew of Fluid Mechanics, 10:221–246.Google Scholar
  9. Lessen, M., Singh, P.J., and Paillet, F. (1974). The stability of a trailing line vortex: Part 1 - inviscid theory. Journal of Fluid Mechanics, 63:753–763.Google Scholar
  10. Mayer, E.W. and Powell, K.G. (1992). Viscous and inviscid instabilities of a trailing vortex. Journal of Fluid Mechanics, 245:91–114.MathSciNetGoogle Scholar
  11. Sherwin, S.J. and Karniadakis, G.E. (1995). A triangular spectral element method: Applications to the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 123:189–229.CrossRefMathSciNetGoogle Scholar
  12. Squire, H.B. (1960). Analysis of the vortex breakdown phenomenon, part I. Report No. 102, Aeronautics Department, Imperial College, London.Google Scholar
  13. Theofilis, V. (2003). Advances in global linear instability analysis of nonparallel and three-dimensional flows. Progress in Aerospace Sciences, 39:249–315.CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Michael S. Broadhurst
    • 1
  • Vassilios Theofilis
    • 2
  • Spencer J. Sherwin
    • 1
  1. 1.Department of AeronauticsImperial College LondonUK
  2. 2.School of AeronauticsUniversidad Politecnica de MadridSpain

Personalised recommendations