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On the determination of vortex ring vorticity using Lagrangian particles

Published online by Cambridge University Press:  17 August 2021

O. Outrata ,
M. Pavelka Open the ORCID record for M. Pavelka [Opens in a new window] ,
J. Hron ,
M. La Mantia Open the ORCID record for M. La Mantia [Opens in a new window] ,
J.I. Polanco Open the ORCID record for J.I. Polanco [Opens in a new window]  and
G. Krstulovic Open the ORCID record for G. Krstulovic [Opens in a new window]
O. Outrata
Affiliation:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic
M. Pavelka
Affiliation:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic
J. Hron
Affiliation:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic
M. La Mantia*
Affiliation:
Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague, Czech Republic
J.I. Polanco
Affiliation:
Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229, F-06304 Nice CEDEX 4, France
G. Krstulovic
Affiliation:
Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Boulevard de l'Observatoire CS 34229, F-06304 Nice CEDEX 4, France
*
†Email address for correspondence: [email protected]
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Abstract

Particles are a widespread tool for obtaining information from fluid flows. When Eulerian data are unavailable, they may be employed to estimate flow fields or to identify coherent flow structures. Here we numerically examine the possibility of using particles to capture the dynamics of isolated vortex rings propagating in a quiescent fluid. The analysis is performed starting from numerical simulations of the Navier–Stokes and the Hall–Vinen–Bekarevich–Khalatnikov equations, respectively describing the dynamics of a Newtonian fluid and a finite-temperature superfluid. The flow-induced positions and velocities of particles suspended in the fluid are specifically used to compute the Lagrangian pseudovorticity field, a proxy for the Eulerian vorticity field recently employed in the context of superfluid $^{4}\textrm {He}$ experiments. We show that, when calculated from ideal Lagrangian tracers or from particles with low inertia, the pseudovorticity field can be accurately used to estimate the propagation velocity and the growth of isolated vortex rings, although the quantitative reconstruction of the corresponding vorticity fields remains challenging. On the other hand, particles with high inertia tend to preferentially sample specific flow regions, resulting in biased pseudovorticity fields that pollute the estimation of the vortex ring properties. Overall, this work neatly demonstrates that the Lagrangian pseudovorticity is a valuable tool for estimating the strength of macroscopic vortical structures in the absence of Eulerian data, which is, for example, the case for superfluid $^{4}\textrm {He}$ experiments.

JFM classification

Vortex Flows: Vortex dynamics Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Quantum fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A44
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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