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
KeywordsNormal Velocity Couette Flow Stable Mode Critical Reynolds Number Eigenfunction Expansion
Unable to display preview. Download preview PDF.
- Henningson, D.S., Johansson, A.V. and Lundbladh, A. 1990 On the evolution of localized disturbances in laminar shear flows. In Laminar — Turbulent Transition 3, ( Eds. Michel, R. and Arnal, D. ), Springer.Google Scholar
- Schensted, I.V. 1961 Contributions to the theory of hydrodynamic stability. Ph.D. Thesis, Univ. Michigan, Ann Arbor.Google Scholar