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
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)