Abstract
In this chapter, I analyze the relative dispersion of a pair of tracer particles with respect to the time asymmetry induced by the irreversibility of turbulent flow. In Sect. 4.1, I use a short-time expansion to obtain a mathematical connection between the mean squared relative separation of a particle pair and the derivative of the squared relative velocity. I briefly explain how this connection can be understood in terms of the irreversibility of the energy cascade and how it determines the time asymmetry observed in pair dispersion. In Sect. 4.2, I describe how the recorded particle track data is analyzed in order to obtain the required time-dependent pair statistics and in Sect. 4.3, I present the experimental results and compare them with data from direct numerical simulation (DNS). Furthermore, I discuss how the finite size of the observation volume leads to a bias of the recorded data and explain which quantities are least affected.
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Notes
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There exists of course the case that a slowly separating particle pair starts very close to the boundary of the observation volume, thus also leading to a short observation time. The starting position at time \(t=0\) is independent of the kinetic properties of the particle pair, however, and thus does not contribute to any form of bias.
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Jucha, J. (2015). Two-Particle Dispersion. In: Time-Symmetry Breaking in Turbulent Multi-Particle Dispersion. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-19192-8_4
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DOI: https://doi.org/10.1007/978-3-319-19192-8_4
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