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 email@example.com Fakultät für Physik, Universität Regensburg, Regensburg, Germany
Journal of Low Temperature Physics – Springer Journals
Published: Mar 7, 2018
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