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On the environmental realizability of algebraically growing disturbances and their relation to Klebanoff modes. (English) Zbl 0910.76014
Summary: A theoretical explanation of some experimentally observed phenomena associated with the so-called Klebanoff modes is obtained by analyzing the flow over a finite thickness flat plate resulting from a small-amplitude distortion imposed on the upstream mean flow. The analysis shows (among other things) how the stretching of the vortex lines around the plate leads to streamwise vorticity at the plate surface, which then produces a streamwise velocity perturbation within the boundary layer that can be related to the experimentally observed Klebanoff mode. The complete evolution of this flow must be found by solving the boundary-region equations, but a limiting analytical solution can also be obtained. Since the initial growth of the boundary-layer disturbance is nearly algebraic, our results demonstrate how the algebraically growing disturbances can be generated by a realistic external-disturbance environment. The relationship between these results and various bypass transition mechanisms is discussed.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76F10 Shear flows and turbulence
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