Addendum to “On the Transition from Potential Flow to Turbulence ...” by M. Niemetz, R. Hänninen, and W. Schoepe, J. Low Temp. Phys. 187, 195 (2017)

Addendum to “On the Transition from Potential Flow to Turbulence ...” by M. Niemetz, R.... J Low Temp Phys (2018) 192:145 https://doi.org/10.1007/s10909-018-1887-2 Addendum to “On the Transition from Potential Flow to Turbulence …” by M. Niemetz, R. Hänninen, and W. Schoepe, J. Low Temp. Phys. 187, 195 (2017) W. Schoepe Received: 7 January 2018 / Accepted: 28 February 2018 / Published online: 7 March 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 It should be mentioned that an interesting conclusion can be drawn from a compar- ison of the normalized mean lifetimes of the turbulent phases τ in Eq. (27) ∗ 2 τ = exp (n ), (1) where n is the number of vortex rings that are shed from the oscillating sphere during one half-period, and in Eq. (30): ∗ 2 τ = exp [(cRe ) ], (2) where c = 1.04 and Re is the superfluid Reynolds number. The accuracy of c is determined by the accuracy of several numerical factors in Eq. (26) and is estimated to be about 10%. That means within our accuracy we may as well set c = 1. Hence, the conclusion is: Re = n. (3) That means, in our experiment the superfluid Reynolds number is given simply by the number of vortex rings that are shed from the sphere in one half-period of oscillation. This is a surprisingly simple result. In a much different context, an equally simple result for Re has been obtained theoretically in 2D superfluid turbulence in a recent work by Reeves et al. Phys. Rev. Lett. 119, 184502 (2017). B W. Schoepe wilfried.schoepe@ur.de Fakultät für Physik, Universität Regensburg, Regensburg, Germany http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Low Temperature Physics Springer Journals

Addendum to “On the Transition from Potential Flow to Turbulence ...” by M. Niemetz, R. Hänninen, and W. Schoepe, J. Low Temp. Phys. 187, 195 (2017)

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Physics; Condensed Matter Physics; Characterization and Evaluation of Materials; Magnetism, Magnetic Materials
ISSN
0022-2291
eISSN
1573-7357
D.O.I.
10.1007/s10909-018-1887-2
Publisher site
See Article on Publisher Site

Abstract

J Low Temp Phys (2018) 192:145 https://doi.org/10.1007/s10909-018-1887-2 Addendum to “On the Transition from Potential Flow to Turbulence …” by M. Niemetz, R. Hänninen, and W. Schoepe, J. Low Temp. Phys. 187, 195 (2017) W. Schoepe Received: 7 January 2018 / Accepted: 28 February 2018 / Published online: 7 March 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 It should be mentioned that an interesting conclusion can be drawn from a compar- ison of the normalized mean lifetimes of the turbulent phases τ in Eq. (27) ∗ 2 τ = exp (n ), (1) where n is the number of vortex rings that are shed from the oscillating sphere during one half-period, and in Eq. (30): ∗ 2 τ = exp [(cRe ) ], (2) where c = 1.04 and Re is the superfluid Reynolds number. The accuracy of c is determined by the accuracy of several numerical factors in Eq. (26) and is estimated to be about 10%. That means within our accuracy we may as well set c = 1. Hence, the conclusion is: Re = n. (3) That means, in our experiment the superfluid Reynolds number is given simply by the number of vortex rings that are shed from the sphere in one half-period of oscillation. This is a surprisingly simple result. In a much different context, an equally simple result for Re has been obtained theoretically in 2D superfluid turbulence in a recent work by Reeves et al. Phys. Rev. Lett. 119, 184502 (2017). B W. Schoepe wilfried.schoepe@ur.de Fakultät für Physik, Universität Regensburg, Regensburg, Germany

Journal

Journal of Low Temperature PhysicsSpringer Journals

Published: Mar 7, 2018

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