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

Extra: temperature differences

0 5 10 15 20 25 30-6

-5

-4

-3

-2

-1

0

1

tem

p di

ffere

nce

(m

K)

flow velocity (cm/s)

T (K) 1.35 1.45 1.65 1.75

The temperature is measured inside the bellows, and the difference is before and during a bellows compression