Mathematics of Turbulent Flow and Comparison with Experiment
Seminar by Bjorn Birnir
We have all noticed that there is a big difference between our fluid (air) environments on a windy and a calm day. This was illustrated by O. Reynolds in experiments over 150 year ago and he called it the difference between turbulent and laminar flow. In 1941 Kolmogorov and Obukhov used this observation to formulate their scaling theory of turbulence, that is the foundation for modern turbulence research and applications. It is the theory that the design of our cars and airplanes is based on among many other things. In 1959 Landau and Lifschitz formulated a mathematical model for a flow in a turbulent environment and three years later, in 1962, Kolmogorov and Obukhov formulated the version of their scaling theory that we use today. It has proven difficult to improve the Kolmogorov-Obukhov (KO) theory. In this lecture we will describe the recent progress in this direction: The stochastic closure theory of turbulence (SCT) and illustrate its comparisons with experiments in homogeneous turbulence and turbulent flow over a boundary. The SCT holds the promise of improving the KO theory to any desired degree of accuracy.