Vortex diffusion and vortex-line hysteresis in radial quantum turbulence

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

“…Here we briefly recall our results for the behavior of L(r) [23], which could be obtained experimentally from the attenuation coefficient of second sound. Introduction of q = Γ/r in (3), and ignoring, for the moment, the terms in α and in α (which will be considered in Section 2.2), allows us to obtain L(r) from:…”

“…We concentrate our attention on dynamical effects, whereas in [22,23] we considered this problem from a thermodynamic point of view, but with less diversity of dynamical equations than in the present paper. In this section we consider the following evolution equation instead of (2):…”

“…As it is known, in Schwarz derivation of Vinen equation, the first term in the right hand size of equation (3) is substituted with γq · IL . The diffusion term in D and the term in α were considered by us in [22,23,25] from a thermodynamic point of view. The original proposal of this section is the term in α , that describes the role of the heat gradient as vortex source.…”

“…We will separately consider the effect of the diffusion term in D (which were already studied in [23]), the term in α , that is considered here from a new perspective and α , which is considered here for the first time. To this purpose we apply equations (3) to a steady-state counterflow of He II between two concentric cylindrical walls at different temperatures as studied in [26], where the author analyzes a rotating annulus driven by radial counterflow in a two dimensional setting.…”

“…Left: Heat flows axially from the inner cylinder (the hotter one), at fixed temperature T 0 , to the outer colder one. The radial temperature profile T (r) depends on the heat flow and the vortex density radial distribution (from [23]). Right: Example of vortex diffusion.…”