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  • 10:00 PM, Friday, 22 Oct 2021


Course Postgraduate
Semester Electives
Subject Code AE844
Subject Title Instability and Transition of Fluid Flows

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- Orr- Sommerfeld 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, quasiperiodicity, subharmonic cascade, intermittency. 

Text Books
References

1. Drazin, P.G. and Reid, W.H., Hydrodynamic stability, Cambridge university press (2004).

2. Drazin, P.G., Introduction to hydrodynamic stability, Cambridge university press (2002).

3. White, F.M. and Corfield, I., Viscous fluid flow, 3rd ed., McGraw-Hill, (2006).

4. Kundu, P., Cohen, I., Dowling, D., Fluid mechanics, 6th ed., Academic Press, New York, NY, (2015).

5. Todreas, N.E. and Kazimi, M.S., Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, CRC press. (2011).

6. Todreas, N.E. and Kazimi, M.S., Nuclear systems II: Elements of thermal hydraulic design (Vol. 2), Taylor & Francis (1990).

7. Strogatz, S.H., Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, CRC Press (2018).