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.