Hydrodynamic Stability (Theoretical investigation of instabilities in fluid dynamical systems and other relevant fields)

- Conservation Laws
- Modal Analysis
- Linear Stability Analysis
- Primary Instabilities in shear flows
- Secondary Instabilities
- Absolute and convective instabilities
- Nonlinear instability
- Non-modal growth (transient growth)
- transition to turbulence
- thermo-acoustic instability

Students shall (i) obtain knowledge of theoretical and physical aspects of linear and non-linear instability (ii) develop an understanding of the general concept of hydrodynamic instability (iii) learn a hierarchy of mathematical approaches to address stability problems from the traditional standpoint of linear normal mode analysis to transient and inherently non-linear growth, (iv) demonstrate the capability of the learned tools in describing the laminar-to-turbulent transition processes, and (v), explain the major transition mechanisms and scenarios by illustrating the relevant examples in the industrial applications or/and natural phenomena such as astrophysical and geophysical flows.

Fluid Mechanics 1 and 2, Boundary-Layer Theory (the latter is not mandatory but helpful)

The module consists of a lecture. The lecture will be given live either in the classroom or online as front-of-class teaching circulating the presentation and class-notes in advance. The lecture will present and explain the theoretical background to hydrodynamic instabilities.
To exercise and show proficiency in applying the different approaches and theories to the mathematical description of modal and non-modal instabilities, as well as ability to apply them to non-linear scenarios like explaining the process leading to laminar-turbulent transition, the students will have to hand in homework problem sets and deliver a project report through hands-on learning by both individual- and team-based activities and implementing numerical schemes and programming.

Multimedial-based front-of-class teaching supported by online material

- Introduction to Hydrodynamic Stability, Drazin, Cambridge University Press (2012). DOI: 10.1017/CBO9780511809064
- Hydrodynamic and Hydromagnetic Stability, Chandrasekhar S., Dover (1990).
- Theory and Computation of Hydrodynamic Stability, Criminale, W.O., Jackson, T.L., and, Joslin, R. D., Cambridge University Press (2010).
- Stability and Transition in Shear Flows, Schmid and Henningson, Springer-Verlag (2001).
- Instabilities of Flows and Transition to Turbulence, Sengupta, T.K., CRC Press (2012). DOI: 10.1201/b11900
- Advances in Transitional Flow Modeling: Applications to Helicopter Rotors Sheng, C., Springer International Publishing (2017). DOI: 10.1007/978-3-319-32576-7

The practical credit requirement for the course consists of (1) submitting 4 sets of homework consisting of analytical and numerical problems (20% of the final grade), (2) presenting a critical evaluation of two published papers on a stability problem (20% of the final grade) and (3) Final written exam (60% of the final grade, duration: 45 mins).
The students have to show proficiency in applying different approaches and theories to the mathematical description of modal and non-modal instabilities. The presented concepts need to be applied to non-linear scenarios as well like explaining the process leading to laminar-turbulent transition.