Ordinary Differential Equations / Dynamical Systems Partial Differential Equations

1. Introduction 1.1 Laminar flow, turbulence and transition 1.2 Bifurcations 2 Stability of confined flows 2.1 Rayleigh¿Benard 2.2 Taylor¿Couette 3 Stability of parallel and quasi-parallel flows 3.1 Spatial, temporal, and spatiotemporal instability 3.2 Viscous and non-viscous instabilities 3.4 Stability of quasi-parallel flows 4 Global and non-modal stability (transient growth) 5 Transition 5.1 Pipes, boundary layers, jets, and mixing layers 5.2 Secondary instabilities, by-pass transition 6 Turbulence 6.1 Statistical description: Reynolds-averaged Navier Stokes and the closure problem. 6.2 Free shear flows: mixing layers, jets, wakes. 6.3 The scales of turbulent flows: the energy cascade 6.4 Wall-bounded flows: channels, pipes and boundary layers. 7 Introduction to turbulence modeling 7.1 DNS 7.2 LES 7.3 RANS

There will be theory lectures to introduce the theory of stability and the physics of transition and turbulence. The students will need to solve simple problems with analytical solution. In addition they will need to solve numerical problems using Matlab or any other programming environment of their choice.