Singularities in turbulent flows: How to observe them?

Abstract

The existence and relevance of finite time singularities of the fluid equations are outstanding problems in turbulent flows at high Reynolds number. Their existence is based on recent analytical studies of the time dependent equations for inviscid flow and it explains well the long known observation of intermittency there. The analysis of hot wire records of a turbulent flow in the wind tunnel of Modane is in fair agreement with this existence of finite time singularities passing by the point of recording. This analysis relies on the behavior of the structure functions of the Eulerian acceleration at increasing exponents. It is completed by the analysis of Lagrangian data coming from a von Karman experiment. A particular choice of multi-correlation functions of the acceleration, called test functions, makes them sensitive to the irreversible character of the dynamics, which is shown to be effective at short time only, that we interpret as a signature of the presence of singular events developing a very large acceleration on a very short time scale before they disappear. This time is of the order of the Kolmogorov dissipation time. Differently the test functions built on the velocity correlation functions display a much longer irreversible signal which we associate to the energy transfer occurring before the dissipation stage inside the isolated spots where singularities are formed.