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Concept of hydrodynamic stability

  • Andrey V. BoikoEmail author
  • Alexander V. Dovgal
  • Genrih R. Grek
  • Victor V. Kozlov
Chapter
  • 1.6k Downloads
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 98)

Abstract

In the beginning of this chapter, based on elementary physical example, a general idea of stability of motion with respect to disturbances is introduced. Then it is conceptualized for fluid dynamic applications. Stability of fluid flows is categorized in regards of the behavior of kinetic energy of a disturbance in time and space. Finally, the notion of critical parameters at which the motion character changes from stable to unstable is formulated.

Keywords

Reynolds Number Critical Reynolds Number Initial Disturbance Hydrodynamic Stability Conditional Stability 
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.

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References

References

  1. Betchov R, Criminale WO (1967) Stability of parallel flows. Academic, New York Google Scholar
  2. Drazin PG, Reid WH (1981) Hydrodynamic stability. Cambridge University Press, Cambridge zbMATHGoogle Scholar
  3. Landau LD, Lifshitz EM (1959) Fluid mechanics. Pergamon, Oxford Google Scholar
  4. Reynolds O (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Philos Trans R Soc Lond A 174:935–982 zbMATHCrossRefGoogle Scholar

Further Reading

  1. van Dyke M (1982) An album of fluid motion. Parabolic Press, Stanford Google Scholar
  2. Galdi GP, Padula M (1990) A new approach to energy theory in the stability of fluid motion. Arch Rat Mech Anal 110:187–286 MathSciNetzbMATHCrossRefGoogle Scholar
  3. Henningson DS, Reddy SC (1994) On the role of linear mechanisms in transition to turbulence. Phys Fluids A 6(3):1396–1398 MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. Huerre P, Monkewitz PA (1990) Local and global instabilities in spatially developing flows. Ann Rev Fluid Mech 22:473–537 MathSciNetADSCrossRefGoogle Scholar
  5. Joseph DD (1976) Stability of Fluid Motion, Springer Tracts on Natural Philosophy, vol 1. Springer–Verlag, Berlin Google Scholar
  6. Schlichting H, Gersten K (2000) Boundary layer theory, 8th edn. Springer–Verlag, Berlin zbMATHGoogle Scholar
  7. Waleffe F (1995) Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys Fluids 7(12):3060–3066 MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Andrey V. Boiko
    • 1
    Email author
  • Alexander V. Dovgal
    • 1
  • Genrih R. Grek
    • 1
  • Victor V. Kozlov
    • 1
  1. 1.Inst. Theoretical & Applied MechanicsRussian Academy of SciencesNovosibirskRussia

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