Advertisement

An Introduction to Hydrodynamic Stability

  • Anubhab Roy
  • Rama Govindarajan
Chapter

Abstract

In this chapter, our objective is twofold: (1) to describe common physical mechanisms which cause flows to become unstable, and (2) to introduce recent viewpoints on the subject. In the former, we present some well-known instabilities, and also discuss how surface tension and viscosity can act as both stabilisers and destabilisers. The field has gone through a somewhat large upheaval over the last two decades, with the understanding of algebraic growth of disturbances, and of absolute instability. In the latter part we touch upon these aspects.

Keywords

Group Velocity Rayleigh Number Shear Flow Couette Flow Vortex Sheet 
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.

References

  1. 1.
    Bale R, Govindarajan R (2009) Transient growth and why you should care about it? Resonance, submittedGoogle Scholar
  2. 2.
    Batchelor GK (1967) Introduction to fluid dynamics. Cambridge University Press, CambridgeMATHGoogle Scholar
  3. 3.
    Chandrasekhar S (1981) Hydrodynamic and hydromagnetic stability. Dover Publications, New YorkGoogle Scholar
  4. 4.
    Chomaz JM (2005) Global instabilities in spatially developing flows: Non-normality and nonlinearity. Annu Rev Fluid Mech 37:357–392MathSciNetCrossRefGoogle Scholar
  5. 5.
    Craik ADD (2004) The origins of water wave theory. Annu Rev Fluid Mech 36:1–28MathSciNetCrossRefGoogle Scholar
  6. 6.
    Craik ADD (2005) George Gabriel Stokes on water wave theory. Annu Rev Fluid Mech 37: 23–42MathSciNetCrossRefGoogle Scholar
  7. 7.
    de Gennes PG, Brochard F, Quere D (2004) Capillarity and wetting phenomena: Drops, bubbles, pearls, waves. Springer, New YorkMATHGoogle Scholar
  8. 8.
    Drazin PG (2002) Introduction to hydrodynamic stability. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  9. 9.
    Eckhardt B, Grossman S, Lohse D (2007) Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders. J Fluid Mech 581:221–250MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Eckhardt B, Schneider TM, Hof B et al (2007) Turbulence transition in pipe flow. Annu Rev Fluid Mech 39:447–468MathSciNetCrossRefGoogle Scholar
  11. 11.
    Farrell BF, Ioannou PJ (1993) Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys Fluids A 5:1390–1400MATHCrossRefGoogle Scholar
  12. 12.
    Friedman B (1990) Principles and techniques of applied mathematics. Dover, New YorkMATHGoogle Scholar
  13. 13.
    Groisman A, Steinberg V (2000) Elastic turbulence in a polymer solution flow. Nature 405:53–55CrossRefGoogle Scholar
  14. 14.
    Ho CM, Huerre P (1984) Perturbed free shear layers. Annu Rev Fluid Mech 16:365–422CrossRefGoogle Scholar
  15. 15.
    Hof B, van Doorne CWH, Westerweel J et al (2004) Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305:1594–1598CrossRefGoogle Scholar
  16. 16.
    Huerre P, Monkewitz PA (1990) Local and global instabilities in spatially developing flows. Annu Rev Fluid Mech 22:473–537MathSciNetCrossRefGoogle Scholar
  17. 17.
    Huerre P, Rossi M (1998) Hydrodynamic instabilities in open flows. In: Godreche C, Manneville P (eds) Hydrodynamics and nonlinear instabilities 81–294, Cambridge University Press, CambridgeCrossRefGoogle Scholar
  18. 18.
    Huerre P (2000) Open shear flow instabilities. In: Batchelor GK, Moffatt HK, Worster MG (eds) Perspectives in fluid dynamics: A collective introduction to current research, Cambridge University Press, LondonGoogle Scholar
  19. 19.
    Landahl MT (1980) A note on an algebraic instability of inviscid parallel shear flows. J Fluid Mech 98:243–251MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Lighthill MJ (1978) Waves in fluids. Cambridge University Press, LondonMATHGoogle Scholar
  21. 21.
    Lindzen RS (1988) Instability of plane parallel shear flow (toward a mechanistic picture of how it works). PAGEOPH 126:103–121CrossRefGoogle Scholar
  22. 22.
    Morozov AN, van Saarloos W (2007) An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows. Phys Rep 447:112–143MathSciNetCrossRefGoogle Scholar
  23. 23.
    Shaqfeh ESG (1996) Purely elastic instabilities in viscometric flows. Annu Rev Fluid Mech 28:129–185MathSciNetCrossRefGoogle Scholar
  24. 24.
    Waleffe F(1995) Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys Fluids 7:3060–3066MathSciNetMATHGoogle Scholar
  25. 25.
    Waleffe F (1997) On a self-sustaining process in shear flows. Phys Fluids 9:883–900CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Engineering Mechanics UnitJawaharlal Nehru Centre for Advanced Scientific ResearchBangaloreIndia

Personalised recommendations