flowing soap films: a novel platform for 2d turbulence experiments

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