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Relative dispersion in free-surface turbulence

Published online by Cambridge University Press:  13 September 2024

Yaxing Li Open the ORCID record for Yaxing Li [Opens in a new window] ,
Yifan Wang ,
Yinghe Qi Open the ORCID record for Yinghe Qi [Opens in a new window]  and
Filippo Coletti Open the ORCID record for Filippo Coletti [Opens in a new window]
Yaxing Li*
Affiliation:
Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, PR China Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland
Yifan Wang
Affiliation:
Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland
Yinghe Qi
Affiliation:
Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland
Filippo Coletti
Affiliation:
Department of Mechanical and Process Engineering, ETH Zürich, 8092 Zürich, Switzerland
*
†Email address for correspondence: yaxingli@zju.edu.cn
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Abstract

We report on an experimental study in which Lagrangian tracking is applied to millions of microscopic particles floating on the free surface of turbulent water. We leverage a large jet-stirred zero-mean-flow apparatus, where the Reynolds number is sufficiently high for an inertial range to emerge while the surface deformation remains minimal. Two-point statistics reveal specific features of the flow, deviating from the classic description derived for incompressible turbulence. The magnitude of the relative velocity is strongly intermittent, especially at small separations, leading to anomalous scaling of the second-order structure functions in the dissipative range. This is driven by the divergent component of the flow, leading to fast approaching/separation rates of nearby particles. The Lagrangian relative velocity shows strong persistence of the initial state, such that the ballistic pair separation extends to the inertial range of time delays. Based on these observations, we propose a classification of particle pairs based on their initial separation rate. When this is much smaller than the relative velocity prescribed by inertial scaling (which is the case for the majority of the observed particle pairs), the relative velocity transitions to a diffusive growth and the Richardson–Obukhov super-diffusive dispersion is recovered.

JFM classification

Mass Transport: Dispersion Turbulent Flows: Homogeneous turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 993 , 25 August 2024 , R2
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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