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Weakly Damped Vortex Flow on the Free Surface of a Normal Helium He-I Layer

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Abstract

The buoyancy-driven thermogravitational Rayleigh–Benard convection (RBC) occurs in a 1–3 cm-deep layer of normal He-I in a wide experimental cell heated from above at temperatures below the liquid 4He density maximum T < Tm ≈ 2.183 K. It is established that the onset of RBC is accompanied by the appearance of a vortex flow on the free He-I surface. The interaction of these vortices between each other and with vertical vortex structures, which are formed in the bulk of the layer in the process of establishment of turbulent RBC, results in the appearance of large-scale vortices (vortex dipole), the dimensions of which were limited by the cell diameter d = 12.4 cm, on the surface. This corresponds to a transition from a 3D- to 2D-layer situation and the formation of an inverse energy cascade in the surface vortex system. As the temperature of the liquid at the cell bottom rises above Tm, the initial convective motion in the bulk of the non-uniformly heated He-I layer rapidly dies out; however, the vortex flow on the free surface of the liquid is maintained even without pumping energy from the bulk. The results of the long-term (up to ~ 800 s) studies on the evolution of the surface vortex system show that the decay of the total energy of the vortex system with time due to the nonlinear interaction between weakly damped large-scale vortices and their interaction with the cell boundaries can be described by the power law E ~ (1/τ)n with the exponent n≈ 1 ÷ 2 in different experiments. In the further observations (up to 2500 s), the appearance of small-scale vortices on a 2.5-cm-deep He-I surface layer was observed. Now, the decay of the total energy of the small-scale vortex system on the surface of a 3D-layer with time due to the viscous losses in the bulk could be described by the exponential law E ~ exp (− t/τ) with the characteristic time of τ ≈ 320 s.

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Acknowledgements

This study was carried out as part of the state assignments of the Osipyan Institute of Solid State Physics RAS. The authors thank A.V. Lokhov for the technical assistance and V.V. Lebedev and I.V. Kolokolov for their interest and discussion of the experimental results. We are grateful to the anonymous referees for their attention and, according to their remarks, have decided to supplement the list of references with three articles [35,36,37] devoted to the discussion of the features of convective heat transfer in condensed helium.

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Authors and Affiliations

  1. Osipyan Institute of Solid State Physics RAS, 142432, Chernogolovka, Russia

    Alexander Pelmenev, Alexander Levchenko & Leonid Mezhov-Deglin

  2. Chernogolovka Branch of Federal Research Centre for Chemical Physics, RAS, 142432, Chernogolovka, Russia

    Alexander Pelmenev

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  1. Alexander Pelmenev
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  2. Alexander Levchenko
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Correspondence to Alexander Pelmenev.

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It is a great honor for us to contribute our paper to the JLTP issue dedicated to the distinguished scientists Prof. D.M. Lee and J.D. Reppy on the occasion of their 90th birthdays. The most famous works of both experimenters are devoted to the study and understanding of the properties of superfluid 3He and 4He: a phase transition from a normal to a superfluid state in 3He [1], a vortex flow of superfluid He-II, including a flow under microgravity conditions [2].

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Pelmenev, A., Levchenko, A. & Mezhov-Deglin, L. Weakly Damped Vortex Flow on the Free Surface of a Normal Helium He-I Layer. J Low Temp Phys 205, 200–217 (2021). https://doi.org/10.1007/s10909-021-02632-5

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