Dynamics of vortices and interfaces in superfluid³He

Abstract

Rapid new developments have occurred in superfluid hydrodynamics since the discovery of a host of unusual phenomena which arise from the diverse structure and dynamics of quantized vortices in 3 He superfluids. These have been studied in rotating flow with NMR measurements which at best provide an accurate mapping of the different types of topological defects in the superfluid order parameter field. Four observations are reviewed here: (1) the interplay of different vortex structures at the first-order interface between the two major superfluid 3 He phases, 3 He-A and 3 He-B; (2) the shear flow instability of this phase boundary, which is now known as the superfluid Kelvin-Helmholtz instability; (3) the hydrodynamic transition from turbulent to regular vortex dynamics as a function of increasing dissipation in vortex motion; and (4) the peculiar propagation of vortex lines in a long rotating column which even in the turbulent regime occurs in the form of a helically twisted vortex state behind a well-developed vortex front. The consequences and implications of these observations are discussed, as inferred from measurements, numerical calculations and analytical work.

Elementary Vortex Processes in Thermal Superfluid Turbulence

“…The working superfluid is 4 He; similar mathematical models are also applicable to 3 He-B, although the typical phenomenology of 3 He-B flows is expected to differ from the 4 He case since the material properties that enter as parameters in these equations differ significantly between the two fluids [8,41]. We fix the temperature at T = 1.3 K so that ν n = 2.3303 × 10 −3 cm 2 /s, h 1 = 0.04093, and h 2 = −0.02175.…”

“…Notwithstanding their generality, the computational complexity of the aforesaid models does not allow the practical computation of large superfluid systems. Hence, macroscopic scale models based on continuum mechanical theory [7][8][9][10][11][12] in which only the hydrodynamic scales are treated have also been employed. In the latter, both superfluid and normal fluid are depicted as continuous systems, although the discrete nature of superfluid vorticity (in the form of isolated vortex lines) is explicitly taken into account.…”

Energy spectra of finite temperature superfluid helium-4 turbulence

“…Although the superfluid is inviscid, it is capable of supporting vortical modes of flow via the appearance of topological defects, also known as, quantized vortices. A complicated tangle of discrete, quantized vortices is refered to as "superfluid turbulence," [2][3][4][5][6][7] and its hydrodynamic description made necessary an extension of the Landau-Tisza model. Notable such extensions are the Hall-Vinen and Gorter-Mellink equations of two-fluid hydrodynamics with vortices.…”

Spreading of superfluid vorticity clouds in normal-fluid turbulence

“…The normal fluid and superfluid constituents interact via mutual friction forces. Both fluids can become turbulent (Vinen & Niemela 2002;Finne et al 2006). However, due to the very different nature of the statistics obeyed by their constituent particles, the corresponding turbulence physics in the two fluids is different.…”