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  <h1 style="padding-left: 0.5em">Soap Film Turbulence</h1>
  <h2 style="padding-left: 1.5em">a laboratory analogy for turbulence in the ocean and atmosphere</h2>
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<p><em>Experiments in Two-Dimensional Turbulence</em></p>

<p>Student Intern: Udit, Westview High School, Portland, Oregon</p>

<h2>Background Concepts (Week 1)</h2>

<h3>Vocabulary</h3>

<ul>
<li>Passive tracer: A substance (e.g., food coloring) which marks fluid parcels and is
carried passively by the fluid.</li>
<li>Vortex or eddy: An area of the fluid that is spinning or rotating.</li>
<li>Molecular diffusion: The slow process of transport in a fluid by random molecular
(Brownian) motion.</li>
<li>Stratification: Layering of fluids of different densities, e.g., hot water floating
atop cold water.</li>
<li>Advection: The transport of the fluid or a passive tracer by the fluid motion itself.</li>
</ul>


<h3>Demonstrations and Examples</h3>

<ul>
<li>Aspect ratio of the atmosphere: 10km to 36000km</li>
<li>Aspect ratio of the ocean: 5km to 6000km, or 1km to 6000km for upper ocean</li>
<li>Put a small amount of cold milk into still hot water in beaker. Use a funnel or
tube to put milk on bottom without disturbing too much the water. Explain about
two transport processes: molecular diffusion and advection (stirring).</li>
<li>Stir the milk layer. It doesn't take much stirring for the milk to be advected
into long filaments. Once these stretch the milk into very fine strands, molecular
diffusion can act more efficiently on these to mix (homogenize) the milk with the
water.</li>
<li>Repeat. Notice swirls and filaments.</li>
<li>Characteristics of turbulence (drawn on board)

<ol>
<li>irregular motion (stirring) that takes blobs of fluid and stretches them out
into long irregular strands or filaments.</li>
<li>transformation of length scales from large blobs to smaller eddys and strands</li>
<li>vortex stretching, which, by conservation of angular momentum, increases rotation
rate of vortices which creates more strecthing and so-on</li>
</ol></li>
<li>Create bubble films and observe.</li>
<li>Aspect ratio of bubble film is very small, 10micro-meter to 10cm.</li>
<li>Nearly two-dimensional flow in the bubble film may be turbulent, but there is no vortex
stretching, so it is very different from three-dimensional flow in the beaker.</li>
</ul>



<h2>Apparatus Design (Week 2)</h2>

<ul>
<li>References mention flow of 3m/s in vertical films. This is too fast to observe
with conventional camera or slow electronics. To prevent the flow from accelerating
so fast, make the film inclined and closer to horizontal.</li>

<li>Primed and spray painted black a plywood board to hold the film. I used a rough
grade of plywood. Should have used a better grade with more finished surface.</li>

<li>Udit drew a grid in pencil on the painted plywood to make it easier to position
items for attachment.</li>

<li>Bought basic materials for $45 at Home Depot. Materials list to come. Hardware
is based on compression fittings for 1/4in. o.d. tubing.</li>

<li>Joint to bucket made by drilling hole which tightly fits tubing hardware. We
had drilled a practice hole near top of bucket, and I cut this out to make a washer
that make the coupling tighter. This still leaked, so I used some (dried) silicone
sealant to make a gasket that, amazingly, sealed up well. Didn't leak even after
pretty vigorous wiggling.</li>

<li>Udit used a large graduated cylinder to graduate the bucket at 2L incrments.</li>
</ul>


<h2>First Flows (Week 3)</h2>

<p class="first">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.</p>

<p>There are several flow instabilities that probably need attention:</p>

<ul>
<li>Nozzle instability. After a while, the nozzle develops a slop drip-like
oscillation that makes it very hard to draw a bubble. Maybe caused by air in
nozzle? May need to pack it with glass wool or similar.</li>
<li>Nozzles. Low flow rates do not yield steady flows. Seems to be a drip mode.</li>
<li>Diverging jet. Is seems like the entire inlet may be instable or bistable.
When you put an obstruction in the flow, it is apparent that there is a back-flow
along the central axis. May need to put in flow diverters to slow down the
divergence of the flow? How to integrate these into the apparatus so they do not
pop the film?</li>
<li>Convergence. There seems to be an instability at the bottom of the channel due
to the convergence. I think the flow rate must increase and generate ripples due,
in essence, to a hydraulic jump. How slow the flow?</li>
</ul>

<p>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.</p>

<p>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?</p>

<p>How to mount a grid to study grid-generated turbulence?</p>


<h2>Apparatus Design (Week 4)</h2>

<h3>Vocabulary</h3>

<ul>
<li>turbulent</li>
<li>laminar</li>
<li>oscilloscope</li>
<li>waveform</li>
<li>hydraulic jump</li>
<li>instability</li>
</ul>


<h3>Demonstrations and Examples</h3>

<ul>
<li>Showed Udit a variety of flow types and instabilities</li>
<li>Discussed changes to nozzle and convergence/divergence geometries</li>
<li>Discussed with Tom the Mach-Zender interferometer</li>
<li>Udit experimenting with <u>xoscope</u> (computer oscilloscope)</li>
<li>Other good programs for visualizing signals: <u>baudline</u> and <u>glscope</u></li>
</ul>



<h2>Experimentation (Week 5)</h2>

<h3>Conical nozzle with smaller guide wires</h3>

<p class="first">The original nozzle, which is simply a 1/8&quot; 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).</p>

<p>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.</p>


<h3>Acoustic excitation</h3>

<p class="first">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.</p>

<p>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.</p>



<h2>Nozzles and photos (Week 6)</h2>

<h3>New nozzle</h3>

<p class="first">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).</p>

<p>Next week we will try a larger conical nozzle with the low-gauge
(thick) monofilament. Also, I found
<a href="http://maartenrutgers.org/">Maartin Rutger's personal web site</a>
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.</p>


<h3>Photos</h3>

<p class="first">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.</p>



<h2>Nozzle Design (Week 7)</h2>

<p class="first">Udit fashioned a much better conical plastic nozzle. Flow is now stable over
a wider range of flow rates.</p>

<p>Also, we experimented with the divergence angle at the top of the flowing sheet.
Smaller angle yield more stable, laminar flow.</p>

<p>There are interesting instabilities at the bottom of the flow path, where the
flow converges and thickens.</p>


<h2>Optimizing Photos (Week 8)</h2>

<p class="first">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.</p>

<p>To reduce light from behind bubble, we had to spray the &quot;flat-black&quot; 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.</p>

<p>Best looking photos are created by abruptly turning off the flow, or reducing it
to a drip mode.</p>


<h2>Grid generated turbulence (Week 9)</h2>

<p class="first">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.</p>

<p>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.</p>


<h2>Photos of grid-generated turbulence (Week 10)</h2>

<p class="first">To generate turbulence in the wake of the comb seems to require good flow
rate, and rather thock film. Colors from the film are <em>much</em> more subdued in
apparent turbulence. Turbulence is hard to discern by eye, though, since it
is moving rather quickly.</p>

<p>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.</p>


<h2>Particle shadow velocimetry (Week 11)</h2>

<p class="first">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.</p>

<p>Renting from Pro Photo Supply: <a href="http://www.prophotosupply.com/p-rental.htm">http://www.prophotosupply.com/p-rental.htm</a></p>



<h2>To Do</h2>

<ul>
<li>Make smaller source bucket</li>
<li>Buy some neoprene gloves! Hands are drying out.</li>
<li>Calibrate the bucket to get flow rate as a function of fluid height.</li>
<li>Compute hydraulic efficiency of tubing and nozzle.</li>
<li>Measure viscosity of standard bubble solutions.</li>
<li>Measure surface tension. Will we need to improvise an apparatus for this?</li>
<li>Does the department have a high speed camera or other measurement equipment?

<ul>
<li>Rechtenwald has Nikon D200 we can borrow</li>
<li>No response to emails re: high speed camera</li>
</ul></li>
<li>How can we seed this flow?</li>
<li>Can we mark surface of film with a bubble-jet printer head (shoot microscopic dots
onto the film)?</li>
<li>Can Udit collect a bunch of bubble film web links?</li>
<li>Photos of apparatus and films</li>
</ul>



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