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.
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References
References
Betchov R, Criminale WO (1967) Stability of parallel flows. Academic, New York
Drazin PG, Reid WH (1981) Hydrodynamic stability. Cambridge University Press, Cambridge
Landau LD, Lifshitz EM (1959) Fluid mechanics. Pergamon, Oxford
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
Further Reading
van Dyke M (1982) An album of fluid motion. Parabolic Press, Stanford
Galdi GP, Padula M (1990) A new approach to energy theory in the stability of fluid motion. Arch Rat Mech Anal 110:187–286
Henningson DS, Reddy SC (1994) On the role of linear mechanisms in transition to turbulence. Phys Fluids A 6(3):1396–1398
Huerre P, Monkewitz PA (1990) Local and global instabilities in spatially developing flows. Ann Rev Fluid Mech 22:473–537
Joseph DD (1976) Stability of Fluid Motion, Springer Tracts on Natural Philosophy, vol 1. Springer–Verlag, Berlin
Schlichting H, Gersten K (2000) Boundary layer theory, 8th edn. Springer–Verlag, Berlin
Waleffe F (1995) Transition in shear flows. Nonlinear normality versus non-normal linearity. Phys Fluids 7(12):3060–3066
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© 2012 Springer Science+Business Media B.V.
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Boiko, A.V., Dovgal, A.V., Grek, G.R., Kozlov, V.V. (2012). Concept of hydrodynamic stability. In: Physics of Transitional Shear Flows. Fluid Mechanics and Its Applications, vol 98. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2498-3_1
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DOI: https://doi.org/10.1007/978-94-007-2498-3_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2497-6
Online ISBN: 978-94-007-2498-3
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