An Alternative Approach to Disturbances in Boundary Layers
By modelling the boundary layer on a flat plate as a piece-wise linear velocity profile it is possible to analyze disturbances in the flow in a systematic manner. The approach is that of an initial-value, boundary-value problem but, unlike classical normal modes employed in stability theory, the solutions here can be obtained in closed form and they are non separable. A specific example is treated where the vertical component of the perturbation velocity is prescribed as a localized pulse initially. The amplitude is then depicted as a function of time and the coordinates of the plane of the flat plate at a fixed vertical location. The role of three-dimensionality and the initial transient period of development — heretofore unknown — are both shown to be of significant importance in the dynamics. An argument is given to strongly suggest that the origin of large-scale oscillations known to be prevelant in turbulent shear flows may well be explained using these bases.
KeywordsBoundary Layer Normal Mode Flat Plate Initial Disturbance Turbulent Shear Flow
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