# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 2001 Seminar Series**

*Transition and turbulence in Shear Flows; The role of uncertainty*

*Abstract*

**The problem of describing transition in wall bounded shear flows such as
channel and boundary layer flows is an important and old problem in
Hydrodynamic Stability. Classical linear hydrodynamic stability theories
provides predictions that are at odds with most experiments where ``natural''
transition occurs. However, in the past decade it has become recognized that a
new analysis of the linearized Navier-Stokes equations yields much more
satisfactory answers. This analysis is known as related to so-called non-normal
transient growth or psuedo-spectral analysis.**

**In this talk, we will review this new hydrodynamic stability theory from
the point of view of quantifying uncertainty. The linearized Navier-Stokes
equations in strongly sheared flows exhibit remarkable sensitivity to dynamical
perturbations and external forcing or noise. We will argue that the right kind
stability analysis must take this uncertainty explicitly into account, and that
in such geometries, transition is not a question only of stability, but
robustness as well. We point out connections with modern Robust Control Theory,
were analysis of uncertainty effects on stability has been heavily studied.**

**We show how this analysis brings out the ubiquitous coherent structures
of stream-wise vortices and streaks as fundamental to the dynamics of the
linearized NS equations. We will also illustrate how distributed wall roughness
can act as a generator of flow disturbances which then initiate transition
scenarios. We discuss the implications of this analysis to flow control.**

### Friday, September 14, 2001

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior
Secretary, 625-8000.