Dynamical System Methods in Fluid Dynamics

Abstract

The workshop was organized around the following classical as well new and emerging techniques. Traditional methods in fluid mechanics continue to be invigorated with the infusion of ideas from dynamical systems, geometric methods, multiscale analysis, new developments in scientific computation, and control theory. The specific themes of the workshop were as follows: Structure of the Meeting. The meeting had a balance of senior researchers, postdoctoral fellows and graduate students. Consistent with the general approach advocated by Oberwolfach, we selected about 20–25 people to give a lecture at the meeting. They suggested students, postdoctoral fellows and junior faculty all of whom participated through two poster sessions. Posters. The poster session was one of the most interesting aspects of the meeting. The organizers decided to award prizes for the best poster and an ad hoc committee (consisting of Friedlander, Haller, Reich, Marsden and Scheurle) was formed to choose the four best posters. This number matched the number of gifts that were available. The winners were (in alphabetical order): Impressions, Connections, Insights. The mixture of participants, from those who were very applied and those who came from a more of a dynamical systems background, but all with a strong mathematical dedication, was very fruitful. Dynamical systems methods have now started to be utilized successfully for the study of complex real fluid systems, from controlled man-made experiments to multi-scale and multivariate natural dynamics, from oceanic motions to flows around jellyfish. Dynamical system approaches are then applied to complex data, models or combinations thereoff. There is a wide range of research opportunities, including the possibilty for new theoretical and methodological progress. Amongst the specific new connections and insights that were gained, the power of dynamical systems ideas, such as invariant manifolds or Lyapunov exponents, seemed to be quite impressive as well as useful in the context of metereology as well as oceanography. The use of dynamical systems ideas in control of fluids (separation and cavity oscillations, for example) was also quite interesting for a number of the participants.