flowing soap films: a novel platform for 2d turbulence experiments
TRANSCRIPT
Flowing soap films:a novel platform for 2D turbulence experiments.
• A new angle on the long standingproblem of turbulence.
• Conceptually simpler, scalar vorticity.
• New physics, no vortex stretching.
Why 2D?
• Interesting to atmospheric science,plasma turbulence.
• An area where there is much theory, but few experiments.
• Disagreements between simulations.
~cm
~µm
~nm
K. J. Mysels, K. Shinoda,and S. Frankel,Soap Films (Pergamon,New York, 1959).
Cyril Isenberg, TheScience of Soap Filmsand Soap Bubbles(Dover, New York, 1992).
Good Books:
What is a Soap Film?
Soap Flow History
M. Gharib, and P. Derango,Physica D37, 406 (1989).
Y. Couder, J. M. Chomaz, and M. Rabaud,Physica D37, 384 (1989).
Mysels'Rainbow
K.J. Mysels, K. Shinoda, andS. Frankel. Soap Films:Studies of their thinning.(Pergamon, NY, 1959)
Weight
SoapSolution
Soap
Soap Film Flow Channel:
Long lived filmsArbitrary sizeControlled velocityControlled thicknessUniform thickness
Quick Film Renewal
Weight
Solution
SoapSolution Solution
a)
b)c)
d)
e)
f)
g)
h)
∆P
I
II
III
xy
Basic Setup
Vertical Soap Film
YX
Z
LASER
Laser Velocimeter
Hot Wire Anemometer
Measurement Techniques
Particle Imaging Velocimetry
0
20
40
60
80
100
120
140
160
0 1 2 3 4
v (m/s)
2.5
2
1.5
1
0.5
00 1 2 3 4
x (cm)
Rutgers et al., Phys. Fluids 8:2847, 1996.
Laminar Velocity Profiles
v (m/s) h (c
m)
3% Atm
FD
A= 0.66 ρair ηair
yv
3/ 2
Reducing Air Drag
Weight
SoapSolution
SoapSolution
Supersonic shock waves
thickness h
Out of plane wave speed:
v = 2σwave ρH
=2O
2σhρ2
∝ h−1/ 2
film speed ∝ h 2 /3
∝ h−1/ 2wave speed
Supersonics
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)
Film speed ~ 200 cm/sec
1 cm/min
Interaction of two vortex streets
1000 FPS video
I
II
III
IV
4 cm
log kki
k-5/3
k-3
∇ × ∂v∂t
+ v ⋅ ∇v = − ∇Pρ + ν∇2v
⇒ Dω
Dt= ω ⋅ ∇v + ν∇2ω
log kki kd
k-5/3
2D3D
Signatures of 2D turbulence
Kolmogorov '41 Kraichnan '67
Decaying 2D turbulence
Forced 2D turbulence
Forced to decaying
0.0001
0.001
0.01
0.1
1
10
100
0.1 1 10
-5/3
-3-3
k/2 (cm-1)
ˆ |vx(
k y)|
2
E(k
) (a
rb. u
nits
)
ADE C B
M. A. Rutgers, PRL 81:2244 (1998)
π∝∝∝∝
x
Power Laws
π
Injection scale
Non-intrusive excitation
Non-intrusive excitation
Shear suppression of turbulence?
shear < eddy
eddy 0.01 sec
shear rate = 100 cm/seccm
Unstable Shear
2.5
2
1.5
1
0.5
00 1 2 3 4
x (cm)
v (m/s)
Stable Shear