Abstract
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.
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Boiko, A.V., Dovgal, A.V., Grek, G.R., Kozlov, V.V. (2012). Theoretical aspects. 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_2
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DOI: https://doi.org/10.1007/978-94-007-2498-3_2
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