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Transition to turbulence in oscillatory superflows

  • The flow of superfluid helium-4 at very low temperatures around an oscillating microsphere has been studied in detail. At small oscillation amplitudes the drag force is linear in velocity amplitude. Above a critical velocity amplitude vc a transition from potential flow to turbulent flow is signaled by a large and nonlinear drag force that scales as (v2 - v2 c ), where vc is found to be independent of temperature (below 1 K) and of driving force. Interestingly, the critical velocity is found to scale as vc ~ √κω, where κ = h/m ≈ 10−7 m2/s (h is Planck's constant and m is the mass of a helium-4 atom) is the circulation quantum of the superfluid vortices and ω/2π is the oscillation frequency ranging from about 120 Hz to 700 Hz. We also observe slightly above vc that the flow pattern is unstable and switches intermittently between potential flow and turbulence. From time series recorded at constant drive and temperature we have investigated the statistical properties of this switching phenomenon. In this talk the universal law vc ~ √κω will be discussed in detail. It can be derived theoretically in various ways: firstly, from a qualitative but very general argument based on the "superfluid Reynolds number" Rs = vl/κ where v is the flow velocity and l is a characteristic length scale, secondly, and in more detail, from Kopnin's equation of the time dependence of the vortex line density, and, finally, we have obtained this law rigorously by dynamical scaling of the equations of motion of vortex dynamics.

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Metadaten
Author:Risto HänninenORCiD, Michael NiemetzORCiDGND, Wilfried SchoepeORCiD
URL / DOI:http://etc14.ens-lyon.fr/openconf/modules/request.php?module=oc_proceedings&action=view.php&a=Accept&id=17
Parent Title (English):ETC 2013 - 14th European Turbulence Conference 2020: 2 September 2013 - 4 September 2013, Lyon, France
Document Type:conference proceeding (article)
Language:English
Year of first Publication:2020
Release Date:2022/07/20
Institutes:Fakultät Elektro- und Informationstechnik
Fakultät Elektro- und Informationstechnik / Labor Datenkommunikation
research focus:Energie und Mobilität
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG