From: Brenda Cook (brenda@math.missouri.edu)
Date: Wed Nov 08 2006 - 10:46:44 CST
COLLOQUIUM
University of Missouri-Columbia
Department of Mathematics
Joe Skufca
Clarkson University
The Edge of Chaos in
a parallel shear flow
Abstract: Plane Couette flow (shear flow between parallel plates), like
pipe flow, can exhibit transient turbulence in some transitional region
between the purely laminar flow and the fully turbulent condition. For
flow conditions within this transitional region, the laminar flow state
is stable, but if it is perturbed, a long turbulent transient may
result. Understand this transition, as well as characterizing the
stability limits of the laminar state remains an important research
question.
This talk will highlight the applicability of dynamical systems and
chaos to the study of turbulent flow, geared toward a general
mathematics audience
In our research, we study the transition between laminar and turbulent
states by exploring a Galerkin representation of a parallel shear flow.
We find that the regions of initial conditions where the lifetimes show
strong fluctuations and a sensitive dependence on initial conditions are
separated from the ones with a smooth variation of lifetimes by an
object in phase space which we call the “edge of chaos.” We describe
techniques to identify and follow this structure, and our results
indicate that the edge is a surface in phase space. For low Reynolds
numbers we find that the surface coincides with the stable manifold of a
periodic orbit, whereas at higher Reynolds numbers it is the stable set
of a higher-dimensional chaotic object. In essence, the edge defines the
stability region for the laminar flow condition. Although our
low-dimensional model provides inadequate resolution to simulate an
actual flow, we describe how our technique can be applied in full
numerical simulations to identify and track this stability boundary.
3:30-4:20 p.m.
Thursday, November 9, 2006
105 General Classroom Building
Refreshments will be served at 3:00 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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