Abstract
A series of Particle Tracking Velocimetry experiments in turbulent flow have
been performed. In Particle Tracking Velocimetry small, passive tracer particles are seeded in the fluid and illuminated. From camera recordings the trajectory of each tracer particle can be reconstructed in three dimensions. This thesis reports on Lagrangian measurements in hydromechanical turbulence. Following only a single particle the diffusive behavior of the Lagrangian second order structure function is observed. Finite size effects of Lagrangian measurements of velocity are discussed. From studying the pdf of temporal velocity increments on a particle trajectory we find strong signatures of intermittent behavior. These reveal themselves as highly non-Gaussian tails in the distributions for small time lags. The scaling exponents of higher order structure functions is calculated and agreement with the multifractal prediction is found. Much focus is on the separation between two particles - both as an initial value problem and as a boundary value problem. Occupation and transit times defined as the time two particles are within a certain distance of each other conditioned on a uniformly distributed initial separation or a fixed separation, respectively, are investigated. We present a simple relation between the occupation and transit times and observe K41 similarity scaling within the inertial range. Simple models are presented and the relevance for zoo-plankton feeding rates is discussed. The dispersion properties of particle pairs are measured with time running both forwards and backwards. An asymmetry is found: backwards dispersion is approximately twice as fast as the corresponding forward. This behavior is explained as a direct consequence of the positiveness of the intermediate eigenvalue of coarse-grained strain. Taking this approach further we find that the stretching rate in the inertial range is self-similar with a characteristic time scale which is a function of the second order Eulerian structure function. The time scale is closely related to the coarse-grained strain for the particular scale in question. A simple stochastic model is constructed based on the principle of self-similarity of stretching rates. For small times backwards and forwards dispersion occur with equal rates. This is the ballistic Batchelor regime and is in a high Reynolds number experiment found to be very robust. Multi-particle statistics have been measured. The principle axes of triangles and tetrahedra are preferentially oriented with the eigenframe of coarsegrained strain. Scaling laws predicted by the K41 similarity theory are observed in the inertial range for coarse-grained quantities.
been performed. In Particle Tracking Velocimetry small, passive tracer particles are seeded in the fluid and illuminated. From camera recordings the trajectory of each tracer particle can be reconstructed in three dimensions. This thesis reports on Lagrangian measurements in hydromechanical turbulence. Following only a single particle the diffusive behavior of the Lagrangian second order structure function is observed. Finite size effects of Lagrangian measurements of velocity are discussed. From studying the pdf of temporal velocity increments on a particle trajectory we find strong signatures of intermittent behavior. These reveal themselves as highly non-Gaussian tails in the distributions for small time lags. The scaling exponents of higher order structure functions is calculated and agreement with the multifractal prediction is found. Much focus is on the separation between two particles - both as an initial value problem and as a boundary value problem. Occupation and transit times defined as the time two particles are within a certain distance of each other conditioned on a uniformly distributed initial separation or a fixed separation, respectively, are investigated. We present a simple relation between the occupation and transit times and observe K41 similarity scaling within the inertial range. Simple models are presented and the relevance for zoo-plankton feeding rates is discussed. The dispersion properties of particle pairs are measured with time running both forwards and backwards. An asymmetry is found: backwards dispersion is approximately twice as fast as the corresponding forward. This behavior is explained as a direct consequence of the positiveness of the intermediate eigenvalue of coarse-grained strain. Taking this approach further we find that the stretching rate in the inertial range is self-similar with a characteristic time scale which is a function of the second order Eulerian structure function. The time scale is closely related to the coarse-grained strain for the particular scale in question. A simple stochastic model is constructed based on the principle of self-similarity of stretching rates. For small times backwards and forwards dispersion occur with equal rates. This is the ballistic Batchelor regime and is in a high Reynolds number experiment found to be very robust. Multi-particle statistics have been measured. The principle axes of triangles and tetrahedra are preferentially oriented with the eigenframe of coarsegrained strain. Scaling laws predicted by the K41 similarity theory are observed in the inertial range for coarse-grained quantities.
| Original language | English |
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| Number of pages | 63 |
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| Publication status | Published - 2006 |