Theoretical aspects

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


When studying the asymptotic stability of the basic flow, it is possible to simplify the problem essentially by reducing the consideration of nonlinear equations of motion to the analysis of linearized equations for disturbances. In this chapter, various aspects of the corresponding theory for the so-called parallel shear flows are expounded beginning from formulation of linear hydrodynamic stability problems in time and space for wavy (modal) disturbances. The classical Gaster’s transformation between these two approaches is explained. The dual role of viscosity for flow instability is outlined. Then, relevance of oblique waves in instability is discussed. Finally, such special issues, important in the following chapters, as bi-orthogonality of modes and completeness of their set are introduced.


Shear Layer Linear Stability Critical Reynolds Number Homogeneous Boundary Condition Neutral Stability 
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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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