A new assessment of the second-order moment of Lagrangian velocity increments in turbulence |
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Authors: | AS Lanotte L Biferale G Boffetta F Toschi |
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Affiliation: | 1. CNR-ISAC and INFN, Sez. Lecce,, 73100 Lecce, Italy;2. Kavli Institute for Theoretical Physics China, CAS, Beijing, 100190 Chinaa.lanotte@isac.cnr.it;4. Department Physics and INFNUniversity of Rome ‘Tor Vergata’,, 00133 Rome, Italy;5. Kavli Institute for Theoretical Physics China, CAS, Beijing, 100190 China;6. Department Physics and INFNUniversity of Torino,, 10125 Torino, Italy;7. Department of Applied Physics and Department of Mathematics &8. Computer ScienceEindhoven University of Technology, Eindhoven, 5600, MB The Netherlands;9. CNR-IAC, 00185 Rome, Italy |
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Abstract: | The behaviour of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the Lagrangian time-fluctuations, it is possible to rephrase the Kolmogorov 4/5-law into a relation predicting the linear (in time) scaling for the second-order Lagrangian structure function. When such a function is directly observed on current experimental or numerical data, it does not clearly display a scaling regime. A parameterisation of the Lagrangian structure functions based on Batchelor model is introduced and tested on data for 3d turbulence, and for 2d turbulence in the inverse cascade regime. Such parameterisation supports the idea, previously suggested, that both Eulerian and Lagrangian data are consistent with a linear scaling plus finite-Reynolds number effects affecting the small- and large timescales. When large-time saturation effects are properly accounted for, compensated plots show a detectable plateau already at the available Reynolds number. Furthermore, this parameterisation allows us to make quantitative predictions on the Reynolds number value for which Lagrangian structure functions are expected to display a scaling region. Finally, we show that this is also sufficient to predict the anomalous dependency of the normalised root mean squared acceleration as a function of the Reynolds number, without fitting parameters. |
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Keywords: | isotropic turbulence homogeneous turbulence direct numerical simulation two-dimensional turbulence |
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