**Abstract:** Helmholtz established the field of hydrodynamic stability with
his pioneering work in 1868. From then on, hydrodynamic stability became
a important tool in understanding various fundamental phenomena in
aeronautics, meteorology, plasma physics, geophysics, biophysics, etc.
However, there are many discrepancies between hydrodynamic stability
theory and experiments. In this talk, I will formulate a framework for
generalized hydrodynamic stability. I will show that there is much more
information in the linearization of Navier-Stokes equations, than purely
eigen values, as the operator is non normal and uncertain. Even though
the linearization is stable, the existence of large transients ($H_2$
norm), large frequency singular plots ($H_\infty$ norm ), small
stability margins with respect to unmodelled dynamics, and large
amplification of disturbances, are all features which are more important
in prediction of the response of Navier-Stokes equations. A host of new
techniques will be introduced in this new framework of generalized
hydrodynamic stability. The above ideas are applied to understanding
some of the mysteries in transition to turbulence in shear flows.
Spectral computations done on Couette flow will be presented.

**Bio:** Kumar Manoj Bobba got his bachelor's degree in Aerospace
Engineering from Indian Institute of Technology-Madras in 1998. He got
his master of science degree from California Institute of Technology in
Aeronautics, in 1999. He will be graduating in june of 2003 with Ph.D in
Aeronautics, Applied and Computational Mathematics, and Control and
Dynamical Systems from California Institute of Technology. His current
research interests are turbulence, thermal fluid sciences, vortex
dynamics, generalized hydrodynamic stability, multi-scale computations,
robust and non-linear control theory, and modern applied mathematics.