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)

• Current topics in fluid mechanics: Aerodynamics (V. Brion – X)  and Optimisation (T. Sayadi – CNAM)    3 ECTS code SU MU5MEF41
• Drops, Bubbles and Co (D. Quéré & C. Baroud -X)    3 ECTS    code SU    MU5MEF17
• Experimental Methods in Fluid Mechanics (R. Monchaux – ENSTA)    3 ECTS    code SU    MU5MEF26
• Geophysical and Astrophysical fluid dynamics (F. Petrélis & C. Gissinger – ENS)   3 ECTS  code SU    MU5MEF18
• Instabilities and control of shear flows (D. Sipp – ONERA)    3 ECTS    code SU    MU5MEF20
• Internal waves (S. Ortiz – ENSTA)    1,5 ECTS    code IPP    MEC664 IW
• Introduction to hydrodynamic instabilities (L. Lesshaft – X)    3 ECTS    code SU    MU5MEF19
• Micro-hydrodynamics (S. Michelin - X)    3 ECTS    code SU    MU5MEF40
• Multiscale Hydrodynamic Phenomena (P.Y Lagrée – SU)    3 ECTS    code SU    MU5MEF15
• Nonlinear waves and pattern formation  (S. Fauve – ENS)    3 ECTS    code SU    MU5MEF27
• Numerical Methods for fluid mechanics (S. Zaleski – SU)    3 ECTS    code SU    MU5MEF16
• Research in lab (teacher from one of the associated labs)     3 ECTS    code SU    MU5MEF24
• Turbulence Dynamics (B. Gallet – ONERA)     3 ECTS    code SU    MU5MEF22
• Vortices in Hydrodynamics (I. Delbende – SU)    3 ECTS    code SU    MU5MEF06

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.

Deadlines

If you reside abroad, first visit the page https://www.campusfrance.org/en . For some countries, there is a very early deadline before which you have to apply for the so-called CEF. The applications begin in December and the deadlines vary country by country, they can be as early as early March for some countries or even earlier, please check. 

To apply, you should also write an email to the program director, Stéphane Zaleski , preferably before the end of April. The applications committee will reply by early March or earlier by email. In some cases the committee will require the student to visit for an interview. If you are approved, the committee will send a support letter that you can use for your CEF interview if you are in a CEF country.

Application file

Formal applications open in May for the academic year 2021-22. It is not possible to apply directly if you are from a CEF country: in that case apply directly through CampusFrance. After the applications open, go to the dedicated web site. Select "M2 Mécanique : Mécanique des fluides Fondements Applications" and go through the steps. Do not forget to fill in the tab "Formulaires complémentaires" and specify "Fluid Mechanics". It you have trouble with this procedure or wish to know whether your applications has a reasonable chance of success write an email to Stéphane Zaleski . Fees for study at Sorbonne University are minimal.

Accommodation

 A lot of informations are available on the website of the "cité internationale universitaire de Paris". If you require help for housing ask well in advance, before May 30.