How to stir turbulence

Abstract

Turbulence is the time-dependent chaotic flow regime that we encounter every day in our environment. A turbulent flow includes a large range of scales which interact with each other in a complex dynamical way. Turbulent flowfields vary randomly in space and time; and are very difficult to analyze, understand and control. Intriguingly, this random flow field is described by the deterministic Navier-Stokes equation. However, so far a closed system of equations could not be produced for the statistical properties of the fluctuating flow. The existence and smoothness of Navier-Stokes equation are not mathematically proven yet. Understanding its solution is one of the seven most important open problems in mathematics identified by the Clay Mathematics Institute (the Millennium problems). A universal theory of turbulence does not exist: it is the last unsolved problem of classical physics. Dealing with turbulent flows is in the center of engineering applications and technological developments. On the other hand, in a physicist’s point of view its universality makes turbulence attractive. Since the pioneering work of Kolmogorov in 1941 a lot of work has been done on the universality of turbulence. His similarity hypotheses form the first statistical theory of turbulence which still remains as the most appropriate universal theory of turbulence although some aspects of it are questioned in the turbulence research community. In this thesis we address fundamental issues of the turbulence problem experimentally; but also indicate the importance of these problems in practical applications, and the directions of further developments. To achieve this goal we do experiments on especially engineered turbulent flows that in this way are tailored to the problem. The experiments have been done in the wind tunnel facility of Eindhoven University of Technology. To generate the proper turbulent flow in the wind tunnel we used an active grid and designed its time-dependent motion for each problem. High-Reynolds-number turbulent flows have been generated with finely tuned properties by stirring the laminar flow of the wind tunnel with innovative designs of active grid protocols. In order to study a specific problem in turbulence not only a flow with specific properties at high Reynolds numbers is needed but also an accurate and fast flow measurement system is necessary. This measurement system should be able to collect long time-series of the fast varying velocity fields. We use a multiple probe array filled with hot-wire sensors to monitor high-Reynolds-number turbulent flow fields locally at high frequencies. The electronics used for the 10 x-wire probes in the array have been optimized for a perfectly simultaneous multiprobe measurement. An intriguing question that we asked is how a turbulent flow responds to perturbations. In other words, when a turbulent flow has been perturbed howmuch itwill remember about the perturbations? Another question which has practical importance is thatwhether there is an optimumfrequency to stir turbulence. These questions are intriguing because how can a chaotic system be perturbed and how one can resonate with a system that has not a dominant time scale. We also experimentally confront the predictions of the above mentioned theory of Kolmogorov which assumes a universality of turbulent flows at the small scales and simply neglects the anisotropy in these scales. Since it is in the center of many turbulence models his theory has great importance for engineering applications.