The Use of Second Sound in Investigations of Quantum Turbulence in He II

Coherent propagation of vortex rings at extremely high Reynolds numbers

“…We here employ (1.4) to estimate the vortex line density L from the experimentally obtained values of relative amplitude. As already noted, this relation is valid only for homogeneous and isotropic tangles, and an error of the order of 10 % is typically associated with it, at least in the range of experimentally accessible vortex line densities -see again Varga et al (2019). Specifically, for polarized vortex tangles, the experimentally accessible quantity becomes the projection L ⊥ of the vortex tangle into the direction of the second sound wave.…”

“…Each sensor consists of two identical transducers mounted on the opposite sides of the channel. The central element of the transducer is a gold-plated membrane that is permeable only to the superfluid component because μm-sized holes on this membrane do not allow the normal component to go through -see Varga et al (2019) for details. Each membrane is coupled capacitively to a brass electrode.…”

“…In addition, the second sound attenuation technique falls short when the amplitude A 0 is measured in an environment containing a significant density of remnant quantized vortices, which are always present in any sufficiently large volume of He II, as noted above. The results obtained from (1.4) are necessarily relative to this remnant density -which is typically of the order of 10 6 m −2 (Varga et al 2019) -and consequently, quantitative comparisons of results obtained in different experimental facilities are not always possible.…”

“…and consequently, Γ = v n x/2 ∝ Re denotes the circulation according to the slug flow model. At this point, before describing the specific methods chosen for the study, it is useful to introduce briefly the second sound attenuation technique, which is employed widely for the analysis of He II flows (Donnelly 2009;Varga et al 2019). It is based specifically on the emission and subsequent detection of second sound waves, which are temperature waves, due to the spatial variation of the liquid temperature, related to the ratio between the densities of the fluid components -the ordinary sound waves (due to the spatial variation of the fluid density) are named in He II first sound waves.…”

“…These wave amplitudes can then be related to the corresponding vortex line density L, the total length of quantized vortices per unit volume. For a homogeneous and isotropic vortex tangle, the approximate relation (Varga et al 2019) can be written as…”