Flowing soap films: a novel platform for 2D turbulence experiments.

Flowing soap films:
a novel platform for 2D turbulence experiments.

Why 2D?
• A new angle on the long standing
problem of turbulence.
• Conceptually simpler, scalar vorticity.
• New physics, no vortex stretching.
• An area where there is much theory,
but few experiments.
• Disagreements between simulations.
• Interesting to atmospheric science,
plasma turbulence.

What is a Soap Film?
~µm
~nm
Good Books:
~cm
K. J. Mysels, K. Shinoda,
and S. Frankel,
Soap Films (Pergamon,
New York, 1959).
Cyril Isenberg, The
Science of Soap Films
and Soap Bubbles
(Dover, New York, 1992).

Soap Flow History
Mysels'
Rainbow
Y. Couder, J. M. Chomaz, and M. Rabaud,
Physica D37, 384 (1989).
K.J. Mysels, K. Shinoda, and
S. Frankel. Soap Films:
Studies of their thinning.
(Pergamon, NY, 1959)
M. Gharib, and P. Derango,
Physica D37, 406 (1989).

Soap
Solution
Soap
Solution
Soap Film Flow Channel:
Long lived films
Arbitrary size
Controlled velocity
Controlled thickness
Uniform thickness
Quick Film Renewal
Weight
Solution
Weight
Soap
Solution

Basic Setup
a)
b)
c)
d)
∆P
e)
I
f)
y
x
II
g)
h)
III

Vertical Soap Film

Measurement Techniques
Z
Y X
Laser Velocimeter
Hot Wire Anemometer
Particle Imaging Velocimetry
LASER

Laminar Velocity Profiles
x (cm)
0 0 1 2 3 4
0.5
1
v (m/s)
1.5
2
h (cm)
v (m/s)
0
0
20
40
60
80
1 2 3 4
100
120
140
2.5
160
Rutgers et al., Phys. Fluids 8:2847, 1996.

3% Atm
Reducing Air Drag
Soap
Solution
F D
A = 0.66
ρ air η air
y
v 3/2
Weight
Soap
Solution

Supersonic shock waves

Supersonics
Out of plane wave speed:
2σ 2σ
v wave = = ∝ h − 1/ 2
ρ 2
ρ H
h
2O
wave speed ∝ h −1/ 2
film speed ∝ h 2/3
thickness h

Vortex Merger
"Measurements of Symmetric
Vortex Merger." K.S. Fine, C.F.
Driscoll, J.H. Malmberg, and T.B.
Mitchell; Phys. Rev. Lett. 67:588
(1991)

Interaction of two vortex streets
1 cm/min
Film speed ~ 200 cm/sec

1000 FPS video
III
I
4 cm
IV
II

Signatures of 2D turbulence
⎛
∇× ⎜
∂v
∂t + v ⋅ ∇v = − ∇P ⎝
ρ
+ ν∇ 2 v
⎞
⎟ ⇒ Dω
⎠ Dt
= ω ⋅∇v + ν∇ 2 ω
3D
2D
k -5/3
k -5/3 k -3
k i
log k
k d
k i
log k
Kolmogorov '41 Kraichnan '67

Decaying 2D turbulence

Forced 2D turbulence

Forced to decaying
100
|v ˆ x (k y )| 2 E(k) (arb. units)
10
1
0.1
0.01
-5/3
E D C B
-3
A
-3
0.001
0.0001
0.1 1 10
k/2 (cm -1 )
M. A. Rutgers, PRL 81:2244 (1998)

Power Laws
x
π
∝∝∝∝

Injection scale
π

Non-intrusive excitation

Non-intrusive excitation

Shear suppression of turbulence?
shear < eddy
eddy
0.01 sec
shear rate = 100 cm/sec
cm
0.5
x (cm)
0 0 1 2 3 4
1
v (m/s)
1.5
Unstable
Shear
2
2.5
Stable Shear