Nonmodal Amplification of
Disturbances in Channel flows of Newtonian and Viscoelastic fluids:
Implications for
Transition and Control
Professor Mihalo Jovanovic
University
of Minnesota
Department
of Electrical and Computer Engineering
Understanding the mechanisms causing
transition to turbulence in wall-bounded shear flows is one of the oldest and
most vexing problems in fluid mechanics. In this talk, a system theoretic
approach is used to model and analyze this problem in channel flows of both
Newtonian and viscoelastic fluids. Amplification of disturbances is studied
from an input-output point of view by analyzing the responses of the velocity
components to spatio-temporal body forces. We utilize a component wise
frequency response analysis to reveal distinct resonant mechanisms for
subcritical transition. In both Newtonian and viscoelastic fluids, the
dominance of stream wise elongated flow patterns is observed which is in stark
contrast to classical results from modal stability analysis. For stream wise
independent perturbations, an explicit Reynolds number (Re) scaling of
frequency responses from different forcing to different velocity components is
developed, showing the same Re-dependence in Newtonian and viscoelastic fluids.
We further demonstrate that elasticity promotes development of flow patterns
with smaller time constants than in Newtonian fluids and that large
amplification can be achieved even in weakly inertial/strongly elastic channel
flows. The latter observation provides a possible route for transition to
`elastic turbulence' and may be exploited to enhance mixing in microfluidic
devices. Finally, we discuss implication of our results to understanding and
controlling transitional wall-bounded shear flows.
Biiosketch: Mihailo Jovanovic
received the Dipl. Ing. and M.S. degrees, both in mechanical engineering, from
the University of Belgrade, Belgrade, Serbia, in 1995 and 1998, respectively,
and the Ph.D. degree in mechanical engineering from the University of
California, Santa Barbara, in 2004. He was a Visiting Researcher with the
Department of Mechanics, the Royal Institute of Technology, Stockholm, Sweden,
from September to December 2004. He joined the University of Minnesota,
Minneapolis, as an Assistant Professor of Electrical and Computer Engineering
in December 2004. His primary research interests are in modeling, analysis, and
control of spatially distributed dynamical systems. Dr. Jovanovic is a member
of IEEE, SIAM, and APS and an Associate Editor of the IEEE Control Systems
Society Conference Editorial Board. He received a CAREER Award from the
National Science Foundation in 2007.
Friday, October 17, 2008
3:30 – 4:30 p.m.
Rm. 1500 EECS