Time-Symmetry Breaking in Turbulent Multi-Particle Dispersion
by Jennifer Jucha
Date of Examination:2014-09-08
Date of issue:2014-10-02
Advisor:Prof. Dr. Eberhard Bodenschatz
Referee:Prof. Dr. Eberhard Bodenschatz
Referee:Prof. Dr. Annette Zippelius
Persistent Address:
http://dx.doi.org/10.53846/goediss-4700
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Abstract
English
In fluid dynamics, the term turbulence usually describes a special state of a continuous medium in which many interacting degrees of freedom are excited. Turbulent flows therefore exhibit strong temporal and spatial fluctuations in velocity, pressure and other flow properties. This behavior can be found in the atmospheric flows that determine our weather and climate, water flows in rivers and oceans, and even in the coffee we drink and the air we breathe. One of the interesting phenomena observed in turbulent flows is their time irreversibility. When milk is stirred into coffee, for example, turbulent flow generates very complicated, interwoven layer structures of the two substances. Reversing the stirring direction does not untangle the produced layers, but instead enhances the complexity of their structure. The initial condition of the two unmixed fluids can never be reproduced. The irreversibility of turbulent flows arises from instabilities that lead to a flux of energy through scales. For a three-dimensional flow, the spatial scale at which energy is injected is always larger than the scale at which it is viscously dissipated. Energy is therefore transported from large to small scales in a cascade-like manner. Reversing the time direction would lead to a change of direction of this energy flux, showing that turbulent flows are not symmetric in time. Since mixing is a good indicator for the irreversibility of a flow, it seems natural to use the dispersion of particle clusters as a tool to analyze time asymmetry. The simplest case is the dispersion of a set of two particles, called relative dispersion. First experimental and numerical studies on the time asymmetry in relative dispersion have indicated that particles separate faster backwards than forwards in time, but no conclusive explanation has been be given. In this thesis, I present a rigorous theoretical connection between the time asymmetry in the short-time evolution of particle clusters and the intrinsic irreversibility of turbulent flows due to the energy cascade. I confirm my theoretical findings with experimental data conducted in a turbulent water flow produced by two counterrotating propellers. Additionally, I examine how a change of the energy cascade, induced by the addition of minute amounts of polymers to the flow, is reflected in the particle dispersion. I present experimental data showing that the addition of polymers to the flow has a significant impact on time asymmetry in both two- and four-particle dispersion.
Keywords: Turbulence; Fluid Dynamics; Irreversibility; Time Asymmetry