Syllabus

Static and dynamic instability, causes and mechanism of instability normal mode analysis, global stability, role of viscosity- dynamical systems, equilibrium points, linearization, concept of limit cycles and other fixed points of a non-linear dynamical system, asymptotic stability and Lyapunov stability, steady and dynamic bifurcations, bifurcations in 1-D and 2-D non-linear dynamical systems, attractor bifurcations for nonlinear evolutions. Concept of linear stability analysis, Linearization of disturbance equations, three-dimensionality, squire transformation, Kelvin-Helmholtz stability, laminar mixing layer, Gaster transformation, centrifugal stability – OrrSommerfeld equations Evolution of flows with increasing Reynolds number, route to chaos and turbulence, instability of flow past a flat plate at zero incidence, jet and shear layer instability. The Boussinesq equations, free-free boundaries, rigid-rigid boundaries, free rigid boundaries. Benard problem, Couette-Benard flow, Rayleigh-Benard convection, Rayleigh-Taylor instability, Marangoni instability Basic aspects of two- phase flows, simple transient flow modelling in two-phase, concept of density wave oscillation, simple model for ledinegg instability, perturbation theory to model density wave oscillation in two-phase flow Temporal chaos in dissipative systems, strange attractors, fractional dimensions, quasiperiodic- ity, subharmonic cascade, intermittency.