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On the time scales and structure of Lagrangian intermittency in homogeneous isotropic turbulence

Published online by Cambridge University Press:  25 March 2019

R. Watteaux Open the ORCID record for R. Watteaux [Opens in a new window] ,
G. Sardina Open the ORCID record for G. Sardina [Opens in a new window] ,
L. Brandt Open the ORCID record for L. Brandt [Opens in a new window]  and
D. Iudicone
R. Watteaux*
Affiliation:
Laboratory of Ecology and Evolution of Plankton, Stazione Zoologica Anton Dohrn, 80121 Naples, Italy
G. Sardina
Affiliation:
Department of Mechanics and Maritime Sciences, Fluid Dynamics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
L. Brandt
Affiliation:
KTH Mechanics, SE-100 44 Stockholm, Sweden
D. Iudicone
Affiliation:
Laboratory of Ecology and Evolution of Plankton, Stazione Zoologica Anton Dohrn, 80121 Naples, Italy
*
†Email address for correspondence: romainwatteaux@gmail.com
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Abstract

We present a study of Lagrangian intermittency and its characteristic time scales. Using the concepts of flying and diving residence times above and below a given threshold in the magnitude of turbulence quantities, we infer the time spectra of the Lagrangian temporal fluctuations of dissipation, acceleration and enstrophy by means of a direct numerical simulation in homogeneous and isotropic turbulence. We then relate these time scales, first, to the presence of extreme events in turbulence and, second, to the local flow characteristics. Analyses confirm the existence in turbulent quantities of holes mirroring bursts, both of which are at the core of what constitutes Lagrangian intermittency. It is shown that holes are associated with quiescent laminar regions of the flow. Moreover, Lagrangian holes occur over few Kolmogorov time scales while Lagrangian bursts happen over longer periods scaling with the global decorrelation time scale, hence showing that loss of the history of the turbulence quantities along particle trajectories in turbulence is not continuous. Such a characteristic partially explains why current Lagrangian stochastic models fail at reproducing our results. More generally, the Lagrangian dataset of residence times shown here represents another manner for qualifying the accuracy of models. We also deliver a theoretical approximation of mean residence times, which highlights the importance of the correlation between turbulence quantities and their time derivatives in setting temporal statistics. Finally, whether in a hole or a burst, the straining structure along particle trajectories always evolves self-similarly (in a statistical sense) from shearless two-dimensional to shear bi-axial configurations. We speculate that this latter configuration represents the optimum manner to dissipate locally the available energy.

JFM classification

Mathematical Foundations: Topological fluid dynamics Turbulent Flows: Turbulence simulation

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JFM Papers
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Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 438 - 481
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© 2019 Cambridge University Press 

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