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The correlation between helicity and turbulent transport in turbulent flows is probed with the use of direct numerical simulation and Lagrangian scalar tracking. Channel flow and plane Couette flow at friction Reynolds number 300 and Lagrangian data along the trajectories of fluid particles and passive particles with Schmidt numbers 0.7 and 6 are used. The goal is to identify characteristics of the flow that enhance turbulent transport from the wall, and how flow regions that exhibit these characteristics are related to helicity. The relationship between vorticity and relative helicity along particle trajectories is probed, and the relationship between the distribution of helicity conditioned on Reynolds stress quadrants is also evaluated. More importantly, the correlation between relative helicity density and the alignment of vorticity with velocity vectors and eigenvectors of the rate of strain tensor is presented. Separate computations for particles that disperse the farthest into the flow field and those that disperse the least are conducted to determine the flow structures that contribute to turbulent dispersion. The joint distribution of helicity and vertical velocity, and helicity and vertical vorticity depends on the location of particle release and the Schmidt number. The trajectories of particles that disperse the least are characterized by a correlation between the absolute value of the relative helicity density and the absolute value of the cosine between the vorticity vector and the eigenvectors of the rate of strain tensor, while the value of this correlation approaches zero for the particles that disperse the most.
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On Galilean invariance of mean kinetic helicity
While kinetic helicity is not Galilean invariant locally, it is known [Moffatt, J. Fluid Mech. 35, 117 (1969)] that its spatial integral quantifies the degree of knottedness of vorticity field lines. Being a topological property of the flow, mean kinetic helicity is Galilean invariant. Here, we provide a direct mathematical proof that kinetic helicity is Galilean invariant when spatially integrated over regions enclosed by vorticity surfaces, i.e., surfaces of zero vorticity flux. We also discuss so-called relative kinetic helicity, which is Galilean invariant when integrated over any region in the flow.
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- PAR ID:
- 10519048
- Publisher / Repository:
- aip.org
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 35
- Issue:
- 12
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0178926
