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Models for transition in shear flow

PDE and Applied Math Seminar

Speaker: Norman Lebovitz, University of Chicago
Location: 1147 MSB
Start time: Wed, Apr 1 2009, 4:10PM

The transition toward turbulence is explored through finding the size and shape of the basin of attraction of the stable equilibrium point representing the unperturbed, laminar, shear flow. The basin boundary is an invariant set representing the threshold for the onset of turbulence. It may contain invariant subsets (equilibrium points, periodic orbits, chaotic invariant sets). In some parts of phase space, this boundary consists of adjacent sheets so close together as to make the complementary set, where turbulence is sustained, essentially unattainable.