Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Prof. Divakar Viswanath |
Affiliation | : | University of Michigan |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
March 18-20,2008 (Tuesday to Thursday) |
Title |
: |
compact course on Dynamics of transition and turbulence in shear flows |
Abstract | : |
The statistical study of turbulence is primarily interested in space and time averages formed in many different ways. A dynamical study would be interested not just in averages but also in the way in which the whole velocity field thought of as a point in phase space, evolves over time. The dynamical point of view is natural in some instances as evidenced by certain striking coherent structures in the near-wall region of turbulent shear flows that were first detected in the 1960s. Although understanding the dynamics of transition and turbulence appear to be very difficult problems, it appears as if a little light on that problem may have been shed by some computations and experiments carried out in the last ten years or so.
These lectures will provide an introduction to
the dynamical study of transition and turbulence. We will show how to
reformulate the Navier-Stokes equation for channels and pipes to get rid of
pressure so that the equation becomes a dynamical system. From that
reformulation, we will derive numerical methods for computing periodic
solutions, relative periodic solutions, steady solutions, and traveling
waves. Some of the periodic solutions reproduce the breakup and re-formation
of streaks observed in the near-wall region. Both recent experiments and
computations suggest that lower-branch traveling waves could be important to
transition to turbulence. That connection, along with other related
developments, will be clarified and explained. |