Introduction to hydrodynamic stability

(20h, 3 ECTS) P. Jordan

This course is an introduction to hydrodynamic stability and aims to provide an understanding of the physics underpinning instability phenomena in fluid mechanics, as well as the theoretical framework and numerical tools necessary to describe these. The course covers both modal and non-modal instability, and it includes a presentation of results from recent research.

It presents tools for the analysis of instabilities that develop in flows. By varying the parameters of a flow (for example, the Reynolds number), we observe regime changes: starting from a laminar (stationary) state, periodic oscillations develop and then, more or less abruptly, the flow becomes turbulent. These changes are the consequence of instabilities that appear successively once a certain threshold is crossed in the parameter space. The aim of this course is to develop the theory of these instabilities and its physical interpretation.