Thermal Detection of Turbulent and Laminar Dissipation in Vortex Front Motion

We report on direct measurements of the energy dissipated in the spin-up of the superfluid component of 3He-B. A vortex-free sample is prepared in a cylindrical container, where the normal component rotates at constant angular velocity. At a temperature of 0.20Tc, seed vortices are injected into the system using the shear-flow instability at the interface between 3He-B and 3He-A. These vortices interact and create a turbulent burst, which sets a propagating vortex front into motion. In the following process, the free energy stored in the initial vortex-free state is dissipated leading to the emission of thermal excitations, which we observe with a bolometric measurement. We find that the turbulent front contains less than the equilibrium number of vortices and that the superfluid behind the front is partially decoupled from the reference frame of the container. The final equilibrium state is approached in the form of a slow laminar spin-up as demonstrated by the slowly decaying tail of the thermal signal.Comment: 12 pages, 5 figures, to appear in Journal of Low Temperature Physic

Vortex core contribution to textural energy in 3He-B below 0.4Tc

Vortex lines affect the spatial order-parameter distribution in superfluid 3He-B owing to superflow circulating around vortex cores and due to the interaction of the order parameter in the core and in the bulk as a result of superfluid coherence over the whole volume. The step-like change of the latter contribution at 0.6Tc (at a pressure of 29bar) signifies the transition from axisymmetric cores at higher temperatures to broken-symmetry cores at lower temperatures. We extended earlier measurements of the core contribution to temperatures below 0.2Tc, in particular searching for a possible new core transition to lower symmetries. As a measuring tool we track the energy levels of magnon condensate states in a trap formed by the order-parameter texture.Comment: 13 pages, 10 figures, submitted to proceedings of the QFS2010 conferenc

The dynamics of vortex generation in superfluid 3He-B

A profound change occurs in the stability of quantized vortices in externally applied flow of superfluid 3He-B at temperatures ~ 0.6 Tc, owing to the rapidly decreasing damping in vortex motion with decreasing temperature. At low damping an evolving vortex may become unstable and generate a new independent vortex loop. This single-vortex instability is the generic precursor to turbulence. We investigate the instability with non-invasive NMR measurements on a rotating cylindrical sample in the intermediate temperature regime (0.3 - 0.6) Tc. From comparisons with numerical calculations we interpret that the instability occurs at the container wall, when the vortex end moves along the wall in applied flow.Comment: revised & extended version. Journal of Low Temperature Physics, accepted (2008

Transition to Superfluid Turbulence

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

Experiments on the twisted vortex state in superfluid 3He-B

We have performed measurements and numerical simulations on a bundle of vortex lines which is expanding along a rotating column of initially vortex-free 3He-B. Expanding vortices form a propagating front: Within the front the superfluid is involved in rotation and behind the front the twisted vortex state forms, which eventually relaxes to the equilibrium vortex state. We have measured the magnitude of the twist and its relaxation rate as function of temperature above 0.3Tc. We also demonstrate that the integrity of the propagating vortex front results from axial superfluid flow, induced by the twist.Comment: prepared for proceedings of the QFS2007 symposium in Kaza

Phase diagram of turbulence in superfluid 3He-B

In superfluid 3He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52--0.59Tc and has a narrow width of 0.06Tc while at zero pressure turbulence is not observed above 0.45Tc.Comment: To be published in J. Low Temp. Phys. (QFS2004 proceedings

Rotating inclined cylinder and the effect of the tilt angle on vortices

We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small tilt angles the vortices tend to align along the cylinder axis and not along the rotation axis. We also show that the axial flow along the cylinder axis, caused by the tilt, will result in the Ostermeier-Glaberson instability above some critical tilt angle. When the vortices become unstable the final state often appears to be a dynamical steady state, which may contain turbulent regions where new vortices are constantly created. These new vortices push other vortices in regions with laminar flow towards the top and bottom ends of the cylinder where they finally annihilate. Experimentally the inclined cylinder could be a convenient environment to create long lasting turbulence with a polarization which can be adjusted with the tilt angle.Comment: 10 pages, 10 figure

Covariant Vortex In Superconducting-Superfluid-Normal Fluid Mixtures with Stiff Equation of State

The integrals of motion for a cylindrically symmetric stationary vortex are obtained in a covariant description of a mixture of interacting superconductors, superfluids and normal fluids. The relevant integrated stress-energy coefficients for the vortex with respect to a vortex-free reference state are calculated in the approximation of a ``stiff'', i.e. least compressible, relativistic equation of state for the fluid mixture. As an illustration of the foregoing general results, we discuss their application to some of the well known examples of ``real'' superfluid and superconducting systems that are contained as special cases. These include Landau's two-fluid model, uncharged binary superfluid mixtures, rotating conventional superconductors and the superfluid neutron-proton-electron plasma in the outer core of neutron stars.Comment: 14 pages, uses RevTeX and amssymb, submitte

Tree method for quantum vortex dynamics

We present a numerical method to compute the evolution of vortex filaments in superfluid helium. The method is based on a tree algorithm which considerably speeds up the calculation of Biot-Savart integrals. We show that the computational cost scales as Nlog{(N) rather than N squared, where $N$ is the number of discretization points. We test the method and its properties for a variety of vortex configurations, ranging from simple vortex rings to a counterflow vortex tangle, and compare results against the Local Induction Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure

The sensitivity of the vortex filament method to different reconnection models

We present a detailed analysis on the effect of using different algorithms to model the reconnection of vortices in quantum turbulence, using the thin-filament approach. We examine differences between four main algorithms for the case of turbulence driven by a counterflow. In calculating the velocity field we use both the local induction approximation (LIA) and the full Biot-Savart integral. We show that results of Biot-Savart simulations are not sensitive to the particular reconnection method used, but LIA results are.Comment: 9 pages, 9 figure