ENGS9Aa.F Transition to turbulence in thermoconvection and aerodynamics  Credits: 2 ECTS Duration: 21 hours  Semester: S9  
Person in charge: Emmanuel Plaut, professor  
Keywords: nonlinear phenomena, stability, instability, bifurcation theory  
Prerequisites: fluid dynamics elementary course, numerical methods  
Objectives: learn relevant nonlinear phenomena in hydrodynamics with heat transfers (thermoconvection) and aerodynamics; learn some methods to model these phenomena.  
Program and contents: The transition to spatiotemporal complexity and turbulence in fluid dynamics, which is intrinsically nonlinear, is studied by focusing on two families of systems. This is also an occasion to enrich the knowledge and knowhow of the students in general fluid mechanics. The families of systems studied are:
Please check the web page of this module on http://emmanuelplaut.perso.univlorraine.fr/t2t : it sketches the planning of this module, gives the lecture notes and instructions, etc... In particular, you will use Mathematica to perform formal (symbolic) and numerical computations on your laptop.  
Abilities :  
Levels  Description and operational vocabulary  
Know  Chaos. The physics of the transition to turbulence in channel flows, boundary layer flows and airfoils  
Understand  Linear vs nonlinear terms  linear vs nonlinear effects. Supercritical vs subcritical bifurcations. The physics of thermoconvection and thermal buoyancy  
Apply  Linear and weakly nonlinear stability analyses. Numerical spectral method  
Analyze  Linear and weakly nonlinear stability analyses. Numerical spectral method  
Summarize  
Assess  
Evaluation:  




