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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 | Abstract: | In 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 | Services: | Forum | Review | PDF | Favorites |
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