Transition to Superfluid Turbulence

Abstract

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid 3He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction -- the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of 1/q < 1 the dynamics is vortex number conserving, while at low friction and large 1/q > 1 vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of 3He-A and 3He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin-Helmholtz instability.Comment: Short review; to be published in Journal of Low Temperature Physics (2006

Universal Mechanism of Dissipation in Fermi Superfluids at Ultralow Temperatures

“…The well known textbook example is the motion of Abrikosov vortices under the action of the Lorentz force which determine the finite resistance of the type-II superconductors 1 . Equally important is the vortex dynamics in the superfluids 4 He and 3 He where motion of quantized vortices mediate the mutual friction force between the normal and superfluid components originating from the scattering of normal excitations by moving vortex lines. The dissipative component of mutual friction provides the relaxation of superflow which is the key aspect in the theory of superfluid turbulence 2 .…”

“…The dissipative component of mutual friction provides the relaxation of superflow which is the key aspect in the theory of superfluid turbulence 2 . Recently there has been a renewal interest in this field owning to the developing experimental techniques allowing to study in particular the decay of quantum turbulence at very low temperatures 3 . In this regime the normal component of the fluid becomes extinct and the mutual friction can not provide the energy dissipation and the relaxation of the superflow.…”

“…This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of 3 He-B the temperature of vortex cores is estimated to be of the order 0.2Tc. The dispersion of Kelvin waves is derived and the heat flow generated by Kelvin cascade is shown to have the value close to the experimentally observed.…”

Rotating trapped Bose-Einstein condensates

“…Consequently, experimental studies provide essential guidance for theoretical analyses. Eltsov et al (2005) and Finne et al (2006) review recent experimental work on vortices and other related structures in superfuid 3 He. In an unbounded dilute trapped BEC with a singlecomponent order parameter, the vortex core size and structure arise from the balance of the kinetic energy and the interaction energy (see Sec.…”

Horizons and Ergoregions in Superfluids

“…25 where also the turbulence triggered in bulk 3 He-B by the interface instabilty is discussed). The important additional feature, which takes place in case of the interface between two sliding superfluids, is the existence of two different critical velocities.…”