Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-25T22:10:13.458Z Has data issue: false hasContentIssue false
  • English
  • Français

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: lamantia@mbox.troja.mff.cuni.cz
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alnæs, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E. & Wells, G.N. 2015 The FEniCS project version 1.5. Arch. Num. Soft. 3, 9–23.Google Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Barenghi, C.F., Skrbek, L. & Sreenivasan, K.R. 2014 Introduction to quantum turbulence. Proc. Natl Acad. Sci. USA 111, 4647–4652.CrossRefGoogle ScholarPubMed
Borner, H. & Schmidt, D.W. 1985 Investigation of large-scale vortex rings in He II by acoustic measurements of circulation. In Flow of Real Fluids (ed. G.E.A. Meier & F. Obermeier), Lecture Notes in Physics, vol. 235, pp. 135–146. Springer.CrossRefGoogle Scholar
Brezzi, F. & Fortin, M. 1991 Mixed and Hybrid Finite Element Methods. Springer.CrossRefGoogle Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. Z. Angew. Math. Phys. 30, 101–116.CrossRefGoogle Scholar
Donnelly, R.J. 2009 The two-fluid theory and second sound in liquid helium. Phys. Today 62 (10), 34–39.CrossRefGoogle Scholar
Donnelly, R.J. & Barenghi, C.F. 1998 The observed properties of liquid helium at the saturated vapor pressure. J. Phys. Chem. Ref. Data 27, 1217–1274.CrossRefGoogle Scholar
Duda, D., La Mantia, M. & Skrbek, L. 2017 Streaming flow due to a quartz tuning fork oscillating in normal and superfluid $^{4}\textrm {He}$. Phys. Rev. B 96, 024519.CrossRefGoogle Scholar
Duda, D., Švančara, P., La Mantia, M., Rotter, M. & Skrbek, L. 2015 Visualization of viscous and quantum flows of liquid $^{4}\textrm {He}$due to an oscillating cylinder of rectangular cross section. Phys. Rev. B 92, 064519.CrossRefGoogle Scholar
Gan, L. & Nickels, T.B. 2010 An experimental study of turbulent vortex rings during their early development. J. Fluid Mech. 649, 467–496.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Glezer, A. 1988 On the formation of vortex rings. Phys. Fluids 31, 3532–3542.CrossRefGoogle Scholar
Guermond, J.L., Minev, P. & Shen, J. 2006 An overview of projection methods for incompressible flows. Comput. Meth. Appl. Mech. Engng 195, 6011–6045.CrossRefGoogle Scholar
Hadjighasem, A. & Haller, G. 2016 Level set formulation of two-dimensional Lagrangian vortex detection methods. Chaos 26, 103102.CrossRefGoogle ScholarPubMed
van Hinsberg, M.A.T., Thije Boonkkamp, J.H.M., Toschi, F. & Clercx, H.J.H. 2012 On the efficiency and accuracy of interpolation methods for spectral codes. SIAM J. Sci. Comput. 34, B479–B498.CrossRefGoogle Scholar
Homann, H., Kamps, O., Friedrich, R. & Grauer, R. 2009 Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows. New J. Phys. 11, 073020.CrossRefGoogle Scholar
La Mantia, M. & Skrbek, L. 2014 Quantum, or classical turbulence? Europhys. Lett. 105, 46002.CrossRefGoogle Scholar
Landau, L. 1941 Theory of the superfluidity of helium II. Phys. Rev. 60, 356–358.CrossRefGoogle Scholar
L'vov, V.S., Nazarenko, S.V. & Skrbek, L. 2006 Energy spectra of developed turbulence in helium superfluids. J. Low Temp. Phys. 145, 125–142.CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227–239.CrossRefGoogle Scholar
Mongiovì, M.S., Jou, D. & Sciacca, M. 2018 Non-equilibrium thermodynamics, heat transport and thermal waves in laminar and turbulent superfluid helium. Phys. Rep. 726, 1–71.CrossRefGoogle Scholar
Niculescu, C.P. & Persson, L.-E. 2006 Convex Functions and their Applications. Springer.CrossRefGoogle Scholar
Nobach, H. & Bodenschatz, E. 2009 Limitations of accuracy in PIV due to individual variations of particle image intensities. Exp. Fluids 47, 27–38.CrossRefGoogle Scholar
Outrata, O. 2020 Numerical methods for vortex dynamics. Master's thesis, Charles University, Prague, Czech Republic.Google Scholar
Polanco, J.I. & Krstulovic, G. 2020 Inhomogeneous distribution of particles in coflow and counterflow quantum turbulence. Phys. Rev. Fluids 5, 032601.CrossRefGoogle Scholar
Raffel, M., Willert, C.E., Scarano, F., Kähler, C.J., Wereley, S.T. & Kompenhans, J. 2018 Particle Image Velocimetry. Springer.CrossRefGoogle Scholar
Sergeev, Y.A. & Barenghi, C.F. 2009 Particles-vortex interactions and flow visualization in $^{4}\textrm {He}$. J. Low Temp. Phys. 157, 429–475.CrossRefGoogle Scholar
Sullivan, I.S., Niemela, J.J., Hershberger, R.E., Bolster, D. & Donnelly, R.J. 2008 Dynamics of thin vortex rings. J. Fluid Mech. 609, 319–347.CrossRefGoogle Scholar
Švančara, P., et al. 2021 Ubiquity of particle-vortex interactions in turbulent counterflow of superfluid helium. J. Fluid Mech. 911, A8.CrossRefGoogle Scholar
Švančara, P., Hrubcová, P., Rotter, M. & La Mantia, M. 2018 Visualization study of thermal counterflow of superfluid helium in the proximity of the heat source by using solid deuterium hydride particles. Phys. Rev. Fluids 3, 114701.CrossRefGoogle Scholar
Švančara, P. & La Mantia, M. 2017 Flows of liquid $^{4}\textrm {He}$due to oscillating grids. J. Fluid Mech. 832, 578–599.CrossRefGoogle Scholar
Švančara, P. & La Mantia, M. 2019 Flight-crash events in superfluid turbulence. J. Fluid Mech. 876, R2.CrossRefGoogle Scholar
Švančara, P., Pavelka, M. & La Mantia, M. 2020 An experimental study of turbulent vortex rings in superfluid $^{4}\textrm {He}$. J. Fluid Mech. 889, A24.CrossRefGoogle Scholar
Villois, A., Proment, D. & Krstulovic, G. 2020 Irreversible dynamics of vortex reconnections in quantum fluids. Phys. Rev. Lett. 125, 164501.CrossRefGoogle ScholarPubMed
Vinen, W.F. & Niemela, J.J. 2002 Quantum turbulence. J. Low Temp. Phys. 128, 167–231.CrossRefGoogle Scholar
Wacks, D.H., Baggaley, A.W. & Barenghi, C.F. 2014 Large-scale superfluid vortex rings at nonzero temperatures. Phys. Rev. B 90, 224514.CrossRefGoogle Scholar