**Dynamics and control of wall-bounded shear flows**

**Speaker:** Mihailo Jovanovic, University of Minnesota

**Series:** MAE Departmental Seminars

**Location:**
Bowen Hall Room 222

**Date/Time: **Friday, October 26, 2012, 3:30 p.m.
- 4:30 p.m.

Understanding and controlling transition to turbulence is one of

the most important problems in fluid mechanics. In the first part

of the talk, techniques from control theory are used to examine the

early stages of transition in wall-bounded shear flows. We

demonstrate high sensitivity of the flow equations to modeling

imperfections and show that control theory can be used not only to

design flow control algorithms but also to provide valuable

insights into the transition mechanisms.

In the second part of the talk, we examine the efficacy of

streamwise traveling waves generated by surface blowing and suction

for controlling the onset of turbulence in a channel flow. For

small amplitude actuation, we utilize weakly-nonlinear analysis to

determine base flow modifications and to assess the resulting net

power balance. Sensitivity analysis of the velocity fluctuations

around this base flow is then employed to design the traveling

waves. Our simulation-free approach reveals that, relative to the

flow with no control, the downstream traveling waves with properly

designed speed and frequency can significantly reduce sensitivity

which makes them well-suited for controlling the onset of

turbulence. In contrast, the velocity fluctuations around the

upstream traveling waves exhibit larger sensitivity to

disturbances. Our theoretical predictions, obtained by perturbation

analysis (in the wave amplitude) of the linearized Navier-Stokes

equations, are verified using simulations of the nonlinear flow

dynamics. These show that a positive net efficiency as large as 25%

relative to the uncontrolled turbulent flow can be achieved with

downstream waves. We conclude that the theory developed for the

linearized flow equations with uncertainty has considerable ability

to predict full-scale phenomena.

**Biography:**

Mihailo R. Jovanovic (www.umn.edu/~mihailo) is an Associate

Professor of Electrical and Computer Engineering at the University

of Minnesota, Minneapolis, where he also serves as the Director of

Graduate Studies in the interdisciplinary Ph.D. program in Control

Science and Dynamical Systems. He has held visiting positions with

Stanford University and the Institute for Mathematics and its

Applications. His current research focuses on sparsity-promoting

optimal control, dynamics and control of fluid flows, and

fundamental limitations in the design of large dynamic networks. He

is a member of IEEE, APS, and SIAM and has served as an Associate

Editor of the IEEE Control Systems Society Conference Editorial

Board from July 2006 until December 2010. He received a CAREER

Award from the National Science Foundation in 2007, an Early Career

Award from the University of Minnesota Initiative for Renewable

Energy and the Environment in 2010, and a Resident Fellowship

within the Institute on the Environment at the University of

Minnesota in 2012.