Dynamics of Polarized Quantum Turbulence in Rotating Superfluid 4He

Paul Walmsley and Andrei Golov

Why study turbulence in rotation?• The effect of polarization of the vortex tangle on the dynamics and decay rate can be studied.

• Steady rotation provides a rectilinear array of vortices. Perturbations, of various types, will allow the dynamics of individual vortex lines (e.g. Kelvin waves) to be probed as well as interactions (such as reconnections) with nearby vortex lines.

• An opportunity to study another type of quasi-classical turbulence. The classical turbulence in a rapidly rotating container has dynamics very different from the isotropic case: the turbulence becomes nearly two-dimensional and the energy spectrum and free-decay laws are changed.

• Container-specific effects such as inertial wave resonances can be investigated.

All experiments used a cubic container. Pulses of negative ions could be fired either along the axis of rotation or transverse to it. T < 0.2 K (i.e. zero temperature limit) for all measurements shown here.

d = 4.5 cm

Experimental cell

Axial

Transverse

5. Axial Measurements in rotationIn rotation, two peaks of current arrive at the top collector following a short injection from the bottom tip:

(1)

(2)

0 0.5 1.0 1.5 2.00

0.5

1.0

1.5

2.0

Cu

rre

nt a

t to

p c

olle

cto

r (p

A)

Time (s)

T = 0.17 K = 1 rad/s0.2 s pulse

(1) Ions along agitated vortices

(2) CVR’s

Steady rotation

agita

tion

Agitation of rectilinear vortex lines can be achieved by: - transverse or axial flow injection; - impulsive redirection of electric field acting on trapped ions;- impulsive spin-up or spin-down to finite W;- AC modulation of W (torsional oscillations).

Spectroscopy by Modulating Rotation

tAC

AC

t

0

Add a oscillatory component of rotation. Both square and sine wave modulations have been tried.

0 10 20 30 400.0

0.2

0.4

0.6

0.8

1.0

square wave sine wave

AC

= 0.0075 rad/s

0 = 0.5 rad/s

0 = 1.0 rad/s

Nor

mal

ised

fas

t pea

k am

plit

ude

0 t

AC

0 = 1.5 rad/s

0 t

AC = 2

Small amplitude modulation: WAC << W0

Resonances observed at particular values of W0 tAC for low frequency modulations.

Collective motion of vortices, most likely to be inertial waves.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20.0

0.2

0.4

0.6

0.8

1.0

square wave sine wave

AC

= 0.0075 rad/s

0 = 0.5 rad/s

0 = 1.0 rad/s

N

orm

alis

ed f

ast

peak

am

plit

ude

mod

/ 20

0 = 1.5 rad/s0.08

0.19 0.30

0.49

Inertial waves

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20.0

0.2

0.4

0.6

0.8

1.0

square wave sine wave

AC

= 0.0075 rad/s

0 = 0.5 rad/s

0 = 1.0 rad/s

N

orm

alis

ed f

ast

peak

am

plit

ude

mod

/ 20

0 = 1.5 rad/s0.08

0.19 0.30

0.49

Inertial waves

Experiments with rotating turbulence:

Experiment with counterflow along rotational axis:Swanson et al. [Phys. Rev. Lett. 50, 190 (1983)]

Numerical simulations:Tsubota, Araki, Barenghi[Phys. Rev. Lett. 90, (2003)]

Transverse Measurements

0.00 0.05 0.10 0.150.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

T = 90 mK, tAC

= 2 / 0

Modulation type: sine wave

0 (rad/s):

0.5 0.75

L /

L0

AC

(rad/s)

The vortex line density, L, was measured using the scattering of a pulse of charged vortex rings fired in the transverse direction. L0 = 2W0 / k – the vortex line density during steady rotation. L / L0 increases as the amplitude of modulation is increased. The axial ion current is the more sensitive probe for small amplitudes of modulation.

Modulating rotation : W from vortex array to turbulence

The behaviour in our T~0 case is probably analogous to the dynamics shown in the numerical simulations of the axial counterflow induced transition from vortex array to turbulence. Tsubota et al., PRL (2003).

When the amplitude of modulation is increased, the fast peak amplitude reaches a maximum before decreasing due to vortices interacting. At high modulation amplitudes, the “fast” peak arrives later and becomes very broad - a state approaching homogeneous turbulence is obtained.

0.00 0.02 0.04 0.06 0.08 0.100

2

4

6

8

10

0 = 1.5 rad/s

tAC

= 2 / 0

T = 95 mK

Am

plit

ud

e a

t co

llect

or

(pA

)

AC

(rad/s)

Depinning of vorticesfrom grid

Onset of turbulence

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

6

7

8

9

10

Cu

rre

nt a

t co

llect

or

(pA

)

t (s)

0 = 1.5 rad/s

tAC

= 2 / 0

AC

(rad/s):

0.0075 0.02 0.035 0.04 0.1

Current transients

Vary amplitude of modulation, WAC

Steady rotation upon spin-down

1 10 100 1000101

102

103

104

T=0.17 K

1 ->

2 (rad/s):

0.15 -> 0 0.20 -> 0.05 0.30 -> 0.15 0.55 -> 0.40 1.15 -> 1.0

L

-L0, cm

-2

t, s

t-3/2

Vortex line density L minus the equilibrium density of the final state L0 = 2 W2 / k

Horizontal probing

Summary

Inertial waves observed for weak perturbations

Increasing the modulation amplitudes leads to a crossover from a weakly perturbed array of rectilinear lines to nearly isotropic 3d turbulence.

The time of flight for ions travelling through the tangle indicates the polarization.

Turbulence produced by oscillatory rotation only decays at late times in an identical manner to turbulence produced by spin down with n = 0.003 k.

Current Generated Turbulence + Rotation

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

Cur

rent

to r

ight

col

lect

or (

pA)

t (s)

T = 90 mK0.2 s pulse, 20 V/cm

0 (rad/s):

0 0.1 0.25 0.5 0.75

"Fast" ions travellingthrough the vortex tangle

Charged vortex rings

Turbulence is generated by injecting current from the left tip during steady rotation, W0. A 0.2 s probe pulse of ions is then fired into the polarized tangle. When there is no rotation, ions arrive quickly as they travel along vortex lines. Increasing W0 slows down the arrival of this peak due to the increased polarization of the tangle inhibiting ion motion in the transverse direction.