Risto Hänninen

Generation of turbulence by oscillating structures in superfluid helium at very low temperatures

The paper is concerned with the interpretation of many experiments that have been reported recently on the production of quantum turbulence by oscillating spheres, wires and grids in both {sup 4}He and {sup 3}He-B at temperatures so low that there is a negligible fraction of normal fluid. The experimental results are compared with those obtained in analogous experiments with classical fluids and with preliminary simulations of the quantum turbulence. Particular attention is paid to observed values of drag coefficients and to the very different critical velocities observed in {sup 4}He and {sup 3}He. It is tentatively concluded that in the case of {sup 4}He behavior may well be similar to that observed in the classical analogues, with relatively small changes when the characteristic size of the oscillating structure is not large compared with the quantized vortex spacing, but that in the case of {sup 3}He behavior is very different and due perhaps to very rapid intrinsic nucleation of the quantized vortices.

Quantum turbulence in a propagating superfluid vortex front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.

Structure of the surface vortex sheet between two rotating 3He superfluids

We study a two-phase sample of superfluid 3He where vorticity exists in one phase (3He-A) but cannot penetrate across the interfacial boundary to a second coherent phase (3He-B). We calculate the bending of the vorticity into a surface vortex sheet on the interface and solve the internal structure of this new type of vortex sheet. The compression of the vorticity from three to two dimensions enforces a structure which is made up of 1 / 2-quantum units, independently of the structure of the source vorticity in the bulk. These results are consistent with our NMR measurements.

Dynamics of vortices and interfaces in superfluid 3he

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 3He 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 3He phases, 3He-A and 3He-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.

Stability and dissipation of laminar vortex flow in superfluid 3He-B.

A central question in the dynamics of vortex lines in superfluids is dissipation on approaching the zero temperature limit T→0. From both NMR measurements and vortex filament calculations, we find that vortex flow remains laminar up to large Reynolds numbers Re{α}∼10(3) in a cylinder filled with 3He-B. This is different from viscous fluids and superfluid 4He, where the corresponding responses are turbulent. In 3He-B, laminar vortex flow is possible in the bulk volume even in the presence of sizable perturbations from axial symmetry to below 0.2Tc. The laminar flow displays no excess dissipation beyond mutual friction, which vanishes in the T→0 limit, in contrast with turbulent vortex motion where dissipation has been earlier measured to approach a large T-independent value at T≲0.2Tc.

Vortex multiplication in applied flow: A precursor to superfluid turbulence.

A surface-mediated process is identified in 3He-B which generates vortices at a roughly constant rate. It precedes a faster form of turbulence where intervortex interactions dominate. This precursor becomes observable when vortex loops are introduced in low-velocity rotating flow at sufficiently low mutual friction dissipation at temperatures below 0.5Tc. Our measurements indicate that the formation of new loops is associated with a single vortex interacting in the applied flow with the sample boundary. Numerical calculations show that the single-vortex instability arises when a helical Kelvin wave expands from a reconnection kink at the wall and then intersects again with the wall.

Universal Critical Velocity for the Onset of Turbulence of Oscillatory Superfluid Flow

AbstractThe critical velocity vc for the onset of turbulent drag of small spheres oscillating in superfluid 4He is frequency dependent (ω/2π from 100 Hz to 700 Hz) and is described by

Anomalous translational velocity of vortex ring with finite-amplitude Kelvin waves.

v_{c}=2.6\sqrt{\kappa \omega}

Superfluid vortex front at T→0: decoupling from the reference frame.

, where κ is the circulation quantum. A qualitative analysis based on a recent theory of the onset of superfluid turbulence gives

Vortex filament method as a tool for computational visualization of quantum turbulence

v_{c}\approx \sqrt{8\kappa \omega/\beta}