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Scaling of Conditional Lagrangian Time Correlation Functions of Velocity and Pressure Gradient Magnitudes in Isotropic Turbulence

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Abstract

We study Lagrangian statistics of the magnitudes of velocity and pressure gradients in isotropic turbulence by quantifying their correlation functions and their characteristic time scales. In a recent work (Yu and Meneveau, Phys Rev Lett 104:084502, 2010), it has been found that the Lagrangian time-correlations of the velocity and pressure gradient tensor and vector elements scale with the locally-defined Kolmogorov time scale, evaluated from the locally-averaged dissipation-rate (ϵ r ) and viscosity (ν) according to \(\tau_{K,r}=\sqrt{\nu/\epsilon_r}\). In this work, we study the Lagrangian time-correlations of the absolute values of velocity and pressure gradients. It has long been known that such correlations display longer memories into the inertial-range as well as possible intermittency effects. We explore the appropriate temporal scales with the aim to achieve collapse of the correlation functions. The data used in this study are sampled from the web-services accessible public turbulence database (http://turbulence.pha.jhu.edu). The database archives a 10244 (space+time) pseudo-spectral direct numerical simulation of forced isotropic turbulence with Taylor-scale Reynolds number Re λ  = 433, and supports spatial differentiation and spatial/temporal interpolation inside the database. The analysis shows that the temporal auto-correlations of the absolute values extend deep into the inertial range where they are determined not by the local Kolmogorov time-scale but by the local eddy-turnover time scale defined as \(\tau_{e,r}= r^{2/3}\epsilon_r^{-1/3}\). However, considerable scatter remains and appears to be reduced only after a further (intermittency) correction factor of the form of (r/L)χ is introduced, where L is the turbulence integral scale. The exponent χ varies for different variables. The collapse of the correlation functions for absolute values is, however, less satisfactory than the collapse observed for the more rapidly decaying strain-rate tensor element correlation functions in the viscous range.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Institute for Data Intensive Engineering and Science, Johns Hopkins University, Baltimore, MD, 21218, USA

    Huidan Yu & Charles Meneveau

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  1. Huidan Yu
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  2. Charles Meneveau
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Correspondence to Huidan Yu.

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The authors are delighted to present this paper in the context of a symposium held in celebration of Professor Stephen B. Pope’s pathbreaking contributions to turbulence and combustion research. They thankfully acknowledge the financial support from the Keck Foundation (L. C.) and the National Science Foundation (ITR-0428325 and CDI-0941530).

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Yu, H., Meneveau, C. Scaling of Conditional Lagrangian Time Correlation Functions of Velocity and Pressure Gradient Magnitudes in Isotropic Turbulence. Flow Turbulence Combust 85, 457–472 (2010). https://doi.org/10.1007/s10494-010-9256-5

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