The Physics of Fluids · 1979 · 116 citations · 4 references
Natural SciencesPhysicsComputational Fluid DynamicsDifferential EquationsFluid DynamicsBoundary ConditionsBoundary Layer FlowBoundary LayersBoundary-layer TheoryBoundary-value ProblemsLaplace Transform MethodsBranch-and-cutInitial Value FormulationInitial Value Problem FormulationLaplace TransformLaplace Transforms Of Differential EquationsTollmien-schlichting WavesVelocityVelocity Profile In Boundary Layers
The behavior of small disturbances in a boundary layer flow is studied. The initial-value problem is solved formally with Fourier–Laplace transforms, and an expression for the development of the velocity component normal to the wall is obtained. It is found that a disturbance evolves not only as discrete waves of the Tollmien–Schlichting type, but also has a portion described by a continuous spectrum. This portion is associated with a branch cut of the solution in the complex plane of the Laplace transform variable.
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