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Lagrangian cascade in three-dimensional homogeneous and isotropic turbulence

Published online by Cambridge University Press:  12 February 2014

Yongxiang Huang  and
François G. Schmitt
Yongxiang Huang*
Affiliation:
Shanghai Institute of Applied Mathematics and Mechanics, and Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, PR China
François G. Schmitt
Affiliation:
Université Lille Nord de France, F-59000 Lille, France USTL, LOG, F-62930 Wimereux, France CNRS, UMR 8187, F-62930 Wimereux, France
*
†Email address for correspondence: [email protected]
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Abstract

In this work, the scaling statistics of the dissipation along Lagrangian trajectories are investigated by using fluid tracer particles obtained from a high-resolution direct numerical simulation with $\mathit{Re}_{\lambda }=400$. Both the energy dissipation rate $\epsilon $ and the local time-averaged $\epsilon _{\tau }$ agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function $\rho (\tau )$ of $\ln (\epsilon (t))$ and variance $\sigma ^2(\tau )$ of $\ln (\epsilon _{\tau }(t))$ obey a log-law with scaling exponent $\beta '=\beta =0.30$ compatible with the intermittency parameter $\mu =0.30$. The $q{\rm th}$-order moment of $\epsilon _{\tau }$ has a clear power law on the inertial range $10<\tau /\tau _{\eta }<100$. The measured scaling exponent $K_L(q)$ agrees remarkably with $q-\zeta _L(2q)$ where $\zeta _L(2q)$ is the scaling exponent estimated using the Hilbert methodology. All of these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Intermittency Turbulent Flows: Isotropic turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 741 , 25 February 2014 , R2
Copyright
© 2014 Cambridge University Press 

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