Fluid mechanics describes the macroscopic motion of fluids, building from first principles of classical physics and thermodynamics. Modern fluid mechanics is a very active research area, driven by its fundamental or curiosity driven research interest as an exemplary complex systems, and by its extreme importance in natural and industrial phenomena.

For the curiosity driven, fluid mechanics offers the example of a complex system in which the basic equations are known (the Navier-Stokes equations have been known for more than a century) but the resulting behavior is hard to predict and complex. Moreover, the very proof of the existence of solutions escapes researchers leading to such tantalizing problems as those being stated by the Clay Prize.

For the application driven, fluid mechanics has long been the province of aircraft designer, "rocket scientists" or automobile designers. However the recent increase in computer power and algorithmic ingenuity, as well as advances in flow visualization, have opened the field to much more numerous applications such as biological and medical engineering, process and chemical engineering, civil engineering, ocean, nuclear or petroleum engineering. The natural science of geophysics, astrophysics and planetary sciences also heavily rely on fluid mechanics.

Fluid phenomena are everywhere. Beyond aerodynamics, meteorology and climatology rest on the predictability of flow phenomena, either for short term weather predictions or for accurate long term modelling of global change. The automotive and petroleum industries have an ever growing need for numerical studies and for talented engineers to set up and interpret the corresponding simulations. The past ten years have seen the opening of the whole new domain of chemical, process and mining engineering to various simulation approaches.

The language of the program is English except for the optional "French for Foreigners" course. As a result the graduate will have the capacity to participate in meetings in English with researchers and engineers of international level. He will be able to read, understand and analyze a recent scientific paper in the general area of fluid mechanics, to evaluate the relevance of the various approximations needed to solve a problem, to implement the numerical modelling of a fluid phenomenon, through the resolution of the Navier-Stokes equations or more specific models, to propose and evaluated numerical resolution methods using research or commercial Computational Fluid Dynamics (CFD) or Computational Multiphase Fluid Dynamics (CMFD) codes such as Gerris, Basilisk or FreeFem.

The second year (which is recommended for most students) of the master is organized as most programs of Sorbonne University. Classes begin around september 20 with several information meetings. The first semester of the second year is organized in two eight-week periods.

1st semester (from September to February) : 10 courses to choose from among :

• Numerical Methods for fluid mechanics, 3 ECTS (S. Zaleski - Sorbonne Université)
• Introduction to hydrodynamic instabilities, 3 ECTS (L. Lesshaft - IPP)
• Experimental Methods, 3 ECTS (R. Monchaux - ENSTA)
• Drops, Bubbles and Co, 3 ECTS (D. Quéré & C. Baroud - IPP)
• Multiscale Hydrodynamic Phenomena, 3 ECTS (P.Y Lagrée – Sorbonne Université)
• Geophysical and Astrophysical fluid dynamics, 3 ECTS (F. Petrélis & C. Gissinger - ENS)
• Turbulence Dynamics, 3 ECTS (B. Gallet – ONERA)
• Nonlinear waves and pattern formation, 3 ECTS (S. Fauve – ENS) 
• Instabilities and control of shear flows, 3 ECTS  (D. Sipp – ONERA)
• Current topics in fluid mechanics, 3 ECTS : Aerodynamics (V. Brion – IPP)  and Optimisation (T. Sayadi – CNAM)
• Micro-hydrodynamics, 3 ECTS (S. Michelin - IPP) 
• Internal waves, 3 ECTS (S. Ortiz – ENSTA) 
• Vortex dynamics,  3 ECTS  (I. Delbende – Sorbonne Université) 
• Non linear fluid dynamics: transport and interfacial dynamics, 3 ECTS  (C. Gissinger - ENS)
• Effect of fluctuations on non linear dynamics, 3 ECTS (F. Petrélis - ENS)
• Research in lab, 3 ECTS

2nd semester (from March on)

• Internship, 30 ECTS (5-6 months)

The program enlists students having a batchelor degree in mechanical engineering, physics or mathematics. Preferably, the batchelor's degree must correspond to four years of university education. A degree of exposure to basic fluid mechanics, numerical methods and to basic classical physics is required, as witnessed by grade transcripts.