Theories of Turbulence
September 17, 2001 — September 21, 2001
Coordinators:
- Martin Oberlack (Techn. Univ. Darmstadt, Darmstadt, Germany)
- Friedrich H. Busse (Univ. Bayreuth - Th. Ph. IV, Bayreuth, Germany)
There is general agreement that the Navier-Stokes equations are capable of describing all properties of turbulence in ordinary fluids. Because of the high Reynolds number of most flows of interest in engineering, atmospheric, oceanographic and astrophysical applications it will not be possible to model these flows through direct numerical simulations in the near future even if the enormous growth of computer capacity continues at the present rate.
Statistical and other kinds of theories of turbulence will increase in importance owing to the desire for a deeper understanding of data obtained from measurements and from computer simulations on the one hand, and because of a strong demand for improved designs in engineering problems and better predictions in atmospheric and oceanographic applications, on the other hand.
The planned course is addressed to a variety of analytical and numerical approaches to problems of turbulent fluid flow with the main goals of providing insights into the nature of turbulence and of presenting methods for obtaining quantitative results in applications. The topics of the lectures range from higher bifurcations and coherent structures through symmetry principles and renormalization theories to Reynolds stress models and sub-grid scale modelling for large eddy simulations. Mathematical tools from group theory and statistics will be presented as needed for the theoretical developments. Applications to examples of turbulent flows in rotating systems and to flows under the influence of magnetic fields will be emphasized throughout the lectures.
The course should be attractive for advanced students and scientists from engineering and applied sciences as well as to physicists and mathematicians interested in the fundamentals of the field.