This page last updated on November 6, 2009.
Experiments in Two-Dimensional Turbulence
Student Intern: Udit, Westview High School, Portland, Oregon
While Udit is gone, I worked with my children (Ava and Milo, ages 7 and 4). We got the basic apparatus to work and drew out some nice stable bubbles.
There are several flow instabilities that probably need attention:
May not have mixed up optimal soap solution (we were excited, and I lost count of ml dish soap per L of water). Also, may want to use glycerin to increase viscosity and slow things down.
Also, there may be more mass near the side wall (fishing line) since the flow seems faster near edges (i.e., more inertial per unit of air drag). Maybe this can be solved with smaller diameter monofilament?
How to mount a grid to study grid-generated turbulence?
The original nozzle, which is simply a 1/8" flat orifice on an end cap, has a drip mode which tends to disrupt the fluid flow. We tried making a more conical nozzle with much thinner guide wires (4 lb-test monofilament vs. 22 lb-test).
The film was much harder to draw out and less stable. Fine droplets formed on the guide wires. Apparently, the flow is more susceptable to a Rayleigh-Plateau-like instability with the finer wires.
Tom, the local mechanical/lab technician, had some previous experience using sound to excite motion in smaller bubble films. We tried using a signal generator and some small speakers to excite the flowing film, and a smaller film drawn in a circular hoop.
This was not particularly successful, but it did give Udit a chance to play with the signal generator. We could only get good coupling between the round film in the hoop and the speaker. And this was just a linear radial mode; no interesting nonlinear flows. Probably the speakers were too small (or maybe the bubble to large) to really couple the sound to the resonances of the bubble.
Udit put together a nozzle based on an airbrush nozzle I found at a craft shop. The orifice was so small that only the high-gauge (thin) monofilament would fit through, hence, it was hard to draw a stable bubble. Also the soap solution came out as a jet which was coherent the entire 1.5m lenght of the film. The film was stable only for small flow diverence setups (approx. 20cm width per meter).
Next week we will try a larger conical nozzle with the low-gauge (thick) monofilament. Also, I found Maartin Rutger's personal web site which shows his apparatus. The divergence from the nozzle is very gentle, apparently just 10cm/1m. And the film flows for well over a meter before going through the test section.
Experimented today with a Nikon D200 digital SLR. We made some very nice photos. Next week: brighter lights and better diffusers! For our work today I used a projector to illuminate a white-board which was used as the light source by reflecting it in the soap film. The camera's autofocus worked surprisingly well.
Udit fashioned a much better conical plastic nozzle. Flow is now stable over a wider range of flow rates.
Also, we experimented with the divergence angle at the top of the flowing sheet. Smaller angle yield more stable, laminar flow.
There are interesting instabilities at the bottom of the flow path, where the flow converges and thickens.
I got a couple of different kinds of translucent plastic, 20% and 60% nominal transittance, according to the plastic shop. Mounted at right-angle to board, so that the plastic acts as a large diffuser. Can aim camera at approx. 30 degrees from normal to fluid sheet and image the colorful bubble very well.
To reduce light from behind bubble, we had to spray the "flat-black" paint, which is remarkably shiny on the primed plywood, onto cardboard. This gets a bit wet and ratty from the soap solution after a while.
Best looking photos are created by abruptly turning off the flow, or reducing it to a drip mode.
Bought hardware that allows us to hold an obstruction in the flow. By analogy to 2-d turbulence, make a grid to generate instabilities and turbulence.
Tried a small plastic comb (0.7mm bars and 1mm gaps), and a comb I made from small wire nails (0.8mm bars and 0.8mm gaps). These are both very hard to introduce into the flowing film without popping it. We had best luck with the plastic comb, getting it very wet, first, and then manually penetrating the film from one edge of the comb to the other.
To generate turbulence in the wake of the comb seems to require good flow rate, and rather thock film. Colors from the film are much more subdued in apparent turbulence. Turbulence is hard to discern by eye, though, since it is moving rather quickly.
It looks like thicker film has more absorption of the multiple internal reflections necessary to generate good color. See theory on Fabry-Perot interferometer. Hmmm. Seem like the two-color intereferometry idea will not work. Can't image much dynamic range of color intensity.
Had to cut out hole in our board to permit imaging light through the film. Using remote flash and plastic diffuser. It is going to take some work to optimize the exposure (distance between flash and diffuser, and other exposure settings). Also, how to focus on the film? The depth of field is very short with 105mm lens at this range.
Renting from Pro Photo Supply: http://www.prophotosupply.com/p-rental.htm
