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Two types of quantum turbulence:mechanically VS thermally driven 4He
superflow in a channel
Simone Babuin, Mathias Stammeier, Miloš Rotter, Ladislav Skrbek
SUPERFLUIDITY GROUPJoint Low Temperature Laboratory
Institute of Physics, Academy of Sciences of the Czech Republic&
Faculty of Mathematics and Physics, Charles University Prague, Czech Republic
The system
(A) Mechanical flow generation: bellows [present work]
(B) Thermal flow generation: counterflow heater
Liquid Helium-4
1.3 K < T < 2.0 K
@ saturated vapour pressure
[Chagovets & Skrbek, PRL 100, 215302 (2008)JLTP 153,162 (2008)]
sq 7 mm
115
mm
Q NS
counterflow
What we measure
1280 1300 1320 1340 1360 1380
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Am
plitu
de (
mV
)
Frequency (Hz)
no flowflow speed 2.6 cm/s
Second sound resonance
0 20 40 60 80 100 120
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
2
4
6
8
10
12
14
16
18
20
22flow starts
Pis
ton
posi
tion
(mm
)
Am
plitu
de (
mV
)
time (s)
flow stops
A0
A
flow speed = 10 cm/s Peak maximum
A0
A
Temperature = 1.45 K
w0
1
6 00
A
A
B
wL
• Scattering of second sound waves against vortex lines• Assume vortex tangle homogeneous and isotropic• Take into account scattering depends on angle
average vortex line length per unit volumeB(T): mutual friction coefficientk: quantum of circulation
Vortex line density
0 2 4 6 8 10 12 14 16 18 20 22 240
500
1000
1500
2000
2500
3000
L1/2 (c
m-1)
flow speed (cm/s)
T (K) 1.35 1.45 1.65 1.75 1.95
0.0 0.5 1.0 1.5 2.00
100
200
300
Open symbols: from full resonant curveFull symbols: from peak maximum
Mechanically driven flow (A)
0 2 4 6 8 10 12 14 16 180
2
4
6
8
10
12
14
L (1
05 c
m-2)
flow speed (cm/s)
Comparison with thermally drive flow
1.49K
1.58K1.73K1.92K
A
B
0 2 4 6 8 10 12 14 16 18102
103
104
105
106
107
TC & LS (2008) T (K)
1.49 1.58 1.73 1.92
L (c
m-2)
flow speed (cm/s)
Present work T(K)
1.351.451.651.751.95
A
B
Slopes
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.10
50
100
150
200
250
300
350
Present work TC&LS (2008) Tough (1981) Schwarz theory
s/cm
2
T (K)
AB
(Schwarz PRB 18 (1978) 245) D
C
Tough et al. PRL 46 (1981) 658
0.13 X 80 mm
C
Critical velocity
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0Present work
direct, ramp up direct, ramp down fit extrapolation
criti
cal v
eloc
ity (
cm/s
)
T (K)
Other works TC&LS (2008) 7mm TC&LS (2008) 10mm Tough PRL 51 2295 (1983)
AB
C
0 40 80 120 160 200 240
5.88
5.90
5.92
5.94
5.96
5.98
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
time (s)
flow
vel
ocity
(cm
/s)
Am
plitu
de s
igna
l (m
V)
Pressure fluct.3 mTorr
Evidence of critical velocity from raw data. Ramping flow velocity UP. T = 1.75 K
0 2 4 6 8 10 12 14 16 18 20 22 240
500
1000
1500
2000
2500
3000
L1/2 (c
m-1)
flow speed (cm/s)
T (K) 1.35 1.45 1.65 1.75 1.95
0.0 0.5 1.0 1.5 2.00
100
200
300
from extrapolation
from direct measurement
A
Summary of the main facts
• A and B disagree in (1), (2) and (3)• A, C and D agree in (1) and (2), but disagree in (3)• B, C and D agree in (3), but disagree in (1) and (2)
A: present work-pure superflow- mechanically
driven- 7x7 mm2 sq
channel- second sound att.
B: TC&LS (2008)- pure superflow- thermally driven- 7x7 mm2 sq
channel- second sound att.
C: Tough (1981)-pure superflow- thermally driven- 0.13 mm circ
channel- temp gradients
D: Schwarz theory (1978)- counterflow in
frame of normal component
- no boundaries
(1) Functional relation between L and v(2) Magnitude of L across whole range of v(3) Critical velocity
Extra: comparison with L from other systems
0 2 4 6 8 10 12 14 16 18 20 22 240
500
1000
1500
2000
2500
3000
T (K) 1.34 1.45 1.65 1.75 1.95 Tough 1.4
L1/2 (c
m-1)
flow speed (cm/s)
0 5 10 15 20 25 301E-3
0.01
0.1
1
inte
r-vo
rte
x sp
aci
ng
(m
m)
flow speed (cm/s)
- used Tough straight line interpolation of 1981 superflow data at T = 1.4 K
- obtained inter-vortex spacing from 1/L1/2
- dashed line indicates size of Tough 1981 channel