An Eigenfunction Expansion of Localized Disturbances
Turbulence inherently involves complicated three-dimensional motions, whereas laminar flow in many instances is two-dimensional. In investigations of the transition process from laminar to turbulent flow, the onset of three-dimensionality has therefore played a major role. The pioneering work of Klebanoff, Tidstrom & Sargent (1962) on the three-dimensional nature of transition in boundary layers started a process which led to the theory of secondary instability. Secondary instability, recently reviewed by Herbert (1988), is able to predict the onset of three-dimensionality as an instability of two-dimensional finite amplitude waves to infinitesimal oblique disturbances. The primary wave is usually taken as the least stable Orr-Sommerfeld (O-S) mode, which is two-dimensional in the Reynolds number range around the onset of growth, i.e. around the critical Reynolds number
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