Statistical Properties of Small Particle Trajectories in a Fully Developed Turbulent State in He-II
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Lagrangian trajectories of small particles in a fully developed turbulent state are studied in a rectangular duct. A plate heater is attached on the bottom to generate the thermal counter flow. The bath temperature is changed from 1.7 to 2.1 K and is controlled within 0.1 mK. Small particles made of solid hydrogen are visualized by high-speed camera, and their trajectories are recorded. Their motions indicate complex features depending not only on bath temperature and heater power, but also on particle size. In this study, the Hurst exponent is defined by \(|\mathbf x (t+\tau )-\mathbf x (t)| \propto \tau ^H\), where \(\mathbf x (t)\) denotes the particle position at time t. It was found that there is a characteristic timescale \(\tau _0\). For small time separation, \(\tau \le \tau _0\), the exponent H is small. However, for large time separation, \(\tau _0 \ll \tau \), H is nearly 1.
KeywordsLagrangian velocity Particle size PTV measurement
Financial support from the Japan Society for the Promotion of Science 15H03917 and Challenging Exploratory Research 16K14158 are gratefully acknowledged. The experimental support by Mr. Akira Hirano, Mr. Daiki Kato and Kouhei Oodaka was indispensable in our measurements.
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