Applied Mathematics Seminar

Applied and Interdisciplinary Mathematics Seminar - Winter 1999
The seminar meets on Monday, 4pm, 3096 East Hall, unless otherwise noted.

Jan 11
Jan 18
Ralf Wittenberg, IMA
TBA
Jan 25
Giovanni Russo
Feb 1
Feb 8
Qi Wang, Indiana University/Purdue University at Indianapolis
TBA
Feb 15
Feb 22
Fabian Waleffe, University of Wisconsin at Madison
"Exact 3D coherent states in plane shear flows"
Mar 1 Spring Break
Mar 8
Mar 15
Nianqing Wang, University of Michigan
Mar 22
Mar 29
Ovidiu Costin, Rutgers University
TBA (exponential asymptotics)
Apr 5
Apr 12
Apr 19

Monday, Jan 18
Ralf Wittenberg, IMA
title TBA

Monday, Feb 8
Qi Wang, Indiana University/Purdue University at Indianapolis

Monday, Feb 22
Fabian Waleffe, University of Wisconsin at Madison
"Exact 3D coherent states in plane shear flows"

Experimentalists have showed the existence of coherent structures in the near wall region of turbulent shear flows over three decades ago. They have drawn various sketches of the structures and described regeneration scenarios in physical terms. A connection between these observations and the Navier-Stokes equations has been lacking but a mathematical formulation for the underlying self-sustaining process is now available. It will be shown how that formulation can be used to calculate exact 3D solutions of the Navier-Stokes equations for both plane Couette and Poiseuille flow. These solutions survive down to Reynolds numbers well below the quoted critical values for transition to turbulence. The solutions are typically unstable and thus inaccessible to experiments and numerical simulations, yet they are remarkably similar to the observed coherent structures. This suggests that they form the "backbone" of the turbulent attractor. A low-order model of the self-sustaining process helps to make sense of these results and guide further investigations.

Monday, Mar 29
Ovidiu Costin, Rutgers University
TBA (exponential asymptotics)