The course is part of the curriculum of the international Master program "Fluid Mechanics, Fundamentals & Applications". It is taught in English and counts for 3 ECTS credit points.

Basic and advanced concepts of linear instability theory are covered:

1) Instability analysis of parallel flows (temporal, spatial, absolute/convective instability)

2) Temporal eigenmode analysis of non-parallel flows

3) Linear input-output analysis of non-parallel flows (the optimal forcing problem)

4) Statistics of stochastically forced turbulent shear flow

The course requires mathematical knowledge of eigenvalue decomposition and Fourier transformation. Homework problems require coding in Matlab/Octave or Python.

Emphasis is placed on shear instability, but boundary layer phenomena and buoyancy-driven instabilities are also covered.

Lutz Lesshafft, Laboratoire d'Hydrodynamique de l'Ecole polytechnique(LadHyX)

lutz.lesshafft@ladhyx.polytechnique.fr

- Teaching coordinator: Josserand Christophe