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Coherent propagation of vortex rings at extremely high Reynolds numbers

Published online by Cambridge University Press:  09 December 2022

P. Švančara Open the ORCID record for P. Švančara [Opens in a new window]  and
M. La Mantia Open the ORCID record for M. La Mantia [Opens in a new window]
P. Švančara*
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
*
†Present address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address for correspondence: [email protected]
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Abstract

We take advantage of the extremely small kinematic viscosity of superfluid $^4$He to investigate the propagation of macroscopic vortex rings at Reynolds numbers between $2 \times 10^4$ and $4 \times 10^6$. These inhomogeneous flow structures are thermally generated by releasing short power pulses into a small volume of liquid, open to the surrounding bath through a vertical tube $2$ mm in diameter. We study specifically the ring behaviour between $1.30$ and $1.80$ K using the flow visualization and second sound attenuation techniques. From the obtained data sets, containing more than $2600$ realizations, we find that the rings remain well-defined in space and time for distances up to at least $40$ tube diameters, and that their circulation depends significantly on the travelled distance, in a way similar to that observed for turbulent vortex rings propagating in Newtonian fluids. Additionally, the ring velocity and circulation appear to be influenced solely by a single, experimentally accessible parameter, combining the liquid temperature with the magnitude and duration of the power pulse. Overall, our results support the view that macroscopic vortex rings moving in superfluid $^4$He closely resemble their Newtonian analogues, at least in the absence of significant thermal effects and at sufficiently large flow scales.

JFM classification

Turbulent Flows: Turbulent Flows Vortex Flows: Vortex dynamics Complex Fluids: Quantum fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 953 , 25 December 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

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., Schmeling, T. & Schmidt, D.W. 1983 Experiments on the circulation and propagation of large-scale vortex rings in He II. Phys. Fluids 26, 1410–1416.CrossRefGoogle Scholar
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
Donnelly, R.J. 1991 Quantized Vortices in Helium II. Cambridge University Press.Google 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
Galantucci, L., Baggaley, A.W., Barenghi, C.F. & Krstulovic, G. 2020 A new self-consistent approach of quantum turbulence in superfluid helium. Eur. Phys. J. Plus 135, 547.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 The formation of vortex rings. Phys. Fluids 31, 3532–3542.CrossRefGoogle Scholar
Glezer, A. & Coles, D. 1990 An experimental study of a turbulent vortex ring. J. Fluid Mech. 211, 243–283.CrossRefGoogle Scholar
Hrubcová, P., Švančara, P. & La Mantia, M. 2018 Vorticity enhancement in thermal counterflow of superfluid helium. Phys. Rev. B 97, 064512.CrossRefGoogle Scholar
Kivotides, D. 2015 Interactions between normal-fluid and superfluid vortex rings in helium-4. Europhys. Lett. 112, 36005.CrossRefGoogle Scholar
Kivotides, D., Barenghi, C.F. & Samuels, D.C. 2005 Measurement of the normal-fluid velocity in superfluids. Phys. Rev. Lett. 95, 215302.CrossRefGoogle ScholarPubMed
Krieg, M. & Mosheni, K. 2021 A new kinematic criterion for vortex ring pinch-off. Phys. Fluids 33, 037120.CrossRefGoogle Scholar
Krueger, P.S., Dabiri, J.O. & Gharib, M. 2006 The formation number of vortex rings formed in uniform background co-flow. J. Fluid Mech. 556, 147–166.CrossRefGoogle Scholar
Kubo, W. & Tsuji, Y. 2019 Statistical properties of small particle trajectories in a fully developed turbulent state in He-II. J. Low Temp. Phys. 196, 170–176.CrossRefGoogle Scholar
Laguna, G.A. 1975 Second-sound attenuation in a supercritical counterflow jet. Phys. Rev. B 12, 4874–4881.CrossRefGoogle Scholar
Landau, L. 1941 Theory of the superfluidity of helium II. Phys. Rev. 60, 356–358.CrossRefGoogle Scholar
Liepmann, H.W. & Laguna, G.A. 1984 Nonlinear interactions in the fluid mechanics of helium II. Annu. Rev. Fluid Mech. 16, 139–177.CrossRefGoogle Scholar
Limbourg, R. & Nedić, J. 2021 Formation of an orifice-generated vortex ring. J. Fluid Mech. 913, A29.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
Murakami, M., Hanada, M. & Yamazaki, T. 1987 Flow visualization study on large-scale vortex ring in He II. Japan J. Appl. Phys. 26 (Suppl. 26-3), 107–108.CrossRefGoogle Scholar
Murakami, M., Yamakazi, T. & Nakai, H. 1989 Laser Doppler velocimeter measurements of thermal counterflow jet in He II. Cryogenics 29, 1143–1147.CrossRefGoogle Scholar
Nakano, A., Murakami, M. & Kunisada, K. 1994 Flow structure of thermal counterflow jet in He II. Cryogenics 34, 991–995.CrossRefGoogle Scholar
Outrata, O., Pavelka, M., Hron, J., La Mantia, M.I., Polanco, J. & Krstulovic, G. 2021 On the determination of vortex ring vorticity using Lagrangian particles. J. Fluid Mech. 924, A44.CrossRefGoogle Scholar
Ricci, M.V. & Vicentini-Missoni, M. 1967 Heat currents in liquid helium II: temperature and velocity fields in large channels. Phys. Rev. 158, 153–161.CrossRefGoogle Scholar
Sakaki, N., Maruyama, T. & Tsuji, Y. 2022 Study on the curvature of Lagrangian trajectories in thermal counterflow. J. Low Temp. Phys. 208, 223–238.CrossRefGoogle Scholar
Stamm, G., Bielert, F., Fiszdon, W. & Piechna, J. 1994 a Counterflow-induced macroscopic vortex rings in superfluid helium: visualization and numerical simulation. Phys. B 193, 188–194.CrossRefGoogle Scholar
Stamm, G., Bielert, F., Fiszdon, W. & Piechna, J. 1994 b On the existence of counterflow induced macroscopic vortex rings in He II. Phys. B 194-196, 589–590.CrossRefGoogle Scholar
Švančara, P. 2021 Experimental investigations of liquid helium flows. PhD thesis, Charles University, Prague, Czech Republic.Google 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. & La Mantia, M. 2017 Flows of liquid $^4$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 $^4$He. J. Fluid Mech. 889, A24.CrossRefGoogle Scholar
Van Sciver, S.W. 2012 Helium Cryogenics. Springer.CrossRefGoogle Scholar
Varga, E., Babuin, S. & Skrbek, L. 2015 Second-sound studies of coflow and counterflow of superfluid $^4$He in channels. Phys. Fluids 25, 065101.CrossRefGoogle Scholar
Varga, E., Jackson, M.J., Schmoranzer, D. & Skrbek, L. 2019 The use of second sound in investigations of quantum turbulence in He II. J. Low Temp. Phys. 197, 130–148.CrossRefGoogle Scholar