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28 March 2024
 
  » arxiv » 1611.9831

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Analysis of the forward and backward in time pair-separation PDFs for inertial particles in isotropic turbulence
Andrew D. Bragg ;
Date 29 Nov 2016
AbstractIn this paper we investigate, using theory and Direct Numerical Simulations (DNS), the Forward In Time (FIT) and Backward In Time (BIT) Probability Density Functions (PDFs) of the separation of inertial particle-pairs in isotropic turbulence. In agreement with our earlier study (Bragg emph{et al.}, Phys. Fluids extbf{28}, 013305 (2016)), where we compared the FIT and BIT mean-square separations, we find that inertial particles separate much faster BIT than FIT, with the strength of the irreversibility depending upon the final/initial separation of the particle-pair and their Stokes number $St$. However, we also find that the irreversibility shows up in subtle ways in the behavior of the full PDF that it does not in the mean-square separation. In the theory, we derive new predictions, including a prediction for the BIT/FIT PDF for ${Stgeq O(1)}$, and for final/initial separations in the dissipation regime. The prediction shows how caustics in the particle relative velocities in the dissipation range affect the scaling of the pair-separation PDF, leading to a PDF with an algebraically decaying tail. The predicted functional behavior of the PDFs is universal, in that it does not depend upon the level of intermittency in the underlying turbulence. We also analyze the dissipation range pair-separation PDFs for fluid particles at short-times, and show that they are given by weighted integrals of functions that decay as stretched exponentials with increasing separation. The weighting function depends upon the local topology of the fluid velocity field, and we derive a simplified result by arguing that the integral should be dominated by regions undergoing strong extensional straining...
Source arXiv, 1611.9831
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