Studies in Global, Bifurcation and Symmetry
Final rept. 1 Dec 88-31 May 91,
CORNELL UNIV ITHACA NY COLL OF ENGINEERING
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Models of Turbulent Boundary Layers used the proper orthogonal decomposition theorem to provide optimal bases for finite dimensional subspaces so that relatively low dimensional projections of the Navier-Stokes equations can be calculated. These dynamical systems retain key features of the turbulence production mechanisms. The inherit symmetries from physical space which lead to the existence of structurally stable heteroclinic cycles, in turn creating intermittent dynamics remarkably similar to the bursting phenomenon observed in experiments. Ours are perhaps the first rationally derived low -10-50 dimensional models for turbulence in open flows and they offer promise of improved understanding of basic mechanisms and design of drag control strategies. Unlike other groups using Karhunen-Loeve methods, we have carried out rather complete analyses of the projected ODEs. This work resulted in papers and also led to the mathematical questions.
- Fluid Mechanics