Marie Farge, Dr. Dr.
Mathematics and Physics, Directeur de recherche
Centre national de la recherche scientifique, Paris
Born in 1953 in Paris
Studied Engineering at Stanford University, Physics at Université Paris VII, and Mathematics at Université Paris VI
Wavelets and TurbulenceI plan to complete the book entitled Wavelets and Turbulence that Cambridge University Press has asked me to write. Turbulence is an open problem for both mathematics and physics, having a lot of applications in engineering. Wavelet theory is a new branch of harmonic analysis that I use to analyze, compute and model turbulent flows.
Farge, Marie. 1986. "L'approche numérique en physique." Fundamenta Scientiae 7, 2: 155-175
Farge, Marie. 1992. "Wavelet transforms and their applications to turbulence." Ann. Rev. Fluid Mech. 24: 395-457.
Farge, Marie and Kai Schneider. 2006. "Wavelets: application to turbulence." Encyclopedia of Mathematical Physics, eds. J. P. Françoise, G. Naber and T. S. Tsun, 408-419. Oxford: Elsevier.
Tuesday Colloquium, 16.02.2010
Can we predict turbulence? In which sense and how?
Turbulence is a physical phenomenon that affects daily life in a wide variety of time and space scales (e.g., blood flow in the heart, cyclones in the atmosphere, magnetic fields of Earth and Sun). Turbulence is a state of flows that is characterized by a chaotic and intermittent behaviour. Although the fundamental equations of fluid dynamics were derived more than three hundred years ago by Leonhard Euler, after Frederic the Great seeked advice from him for the fountains of Sanssouci, it has not yet been proven that their solutions exist when the fluid flow becomes turbulent. This is one of the seven "Millenium Prize" problems of pure mathematics, which were announced in the year 2000 as a follow-up to the 23 problems that Hilbert proposed in 1900 for the twentieth century. The difficulty arises from the highly nonlinear behaviour of turbulent flows, that hinders predicting their evolution. Turbulence is still an open problem of classical mechanics that mathematicians, physicists and engineers tackle by performing both laboratory and numerical experiments. One performs experiments by directly solving the equations using supercomputers and looks for ways of solving them more efficiently. Among those the wavelet representation allows one to grasp at once all the scales where the nonlinear dynamics is active. Wavelets were invented in 1984 by Alex Grossmann (a theoretical physicist working on quantum mechanics) together with Jean Morlet (an engineer working for petroleum exploration). It is now a new branch of mathematics that has been developing very quickly and has already entered daily life (e.g., JPEG 2000 for image compression). This new multiscale viewpoint may offer a useful intellectual tool to study problems, even beyond natural sciences.
Publications from the Fellows' Library
Farge, Marie (2020)