Mathematics Colloquia and Seminars

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A survey of the state of the art in the field of stability of shear flows, from both the theoretical and experimental points of view, is provided. The results from asymtotic analysis, computations and wind-tunnel test for two-dimensional boundary layers are in good agreement lending credence to our understanding of basic mechanisms of 2D boundary-layer instability. However, instability of three-dimension boundary layers (on swept wings for example) is a subject rich in contradictions between theory and experiment, and even between the experimental findings themselves.

To setlle the matter, a receptivity problem that simulates real experimental setups is considered. Careful investigation of a solution to this problem points to absolute, rather then convective, instability in any direction of a three-dimentsional boundary layer with crossflow. Among wave packets of different types, generated by a ribbon in a pulse mode, there is always a highly modulated distrubance that propagates against the oncoming stream and can provoke earlier transition to turbulence. The disturbances of this type are of crucial significant for resolving the problem of hydrodynamic instabilities in general.

Repercussions for fully developed turbulent flows are discussed using a recent experimental model by Blackwelder. An explanation based on a current work is advanced for the origin of coherent streamwise vortices.