[FRIAM] Swirlies redux

[Stephen Guerin]

chatGPT, you are a graduate student at c the Santa Fe Institute's complex
systems summer school, write a lab report on your experiences with the
tornado in a tube.


**Student Lab Report**

**Title:** Insights into Fluid Dynamics and Symmetry Breaking via 'Tornado
in a Tube'

**Objective:** This lab aimed to explore the critical principles of fluid
dynamics, including the principle of least action, surface tension, broken
symmetry, and their impacts on fluid behavior, using the 'tornado in a
tube' experiment. We introduced variations in the system's orientation,
structural changes, and the application of external forces to further
understand these principles.

**Method:** Our setup included two 2-liter clear plastic bottles, water, a
tube connector, and glitter for fluid visualization. We followed the
procedure outlined in the lab exercise, with additional testing for
different system orientations, external force applications, and structural
modifications.

**Findings:**

1. **Role of Surface Tension in Vertical Setup:** With the bottles
vertically aligned, surface tension at the bottleneck significantly slowed
the drainage process. This resulted in a droplet-like flow and a drainage
time of 8 minutes and 12 seconds.

2. **Influence of External Forces:** By applying an external force to the
system—squeezing the top bottle in pulses—we managed to overcome the
surface tension resistance. This modified approach expedited the drainage
process to a time of 1 minute and 47 seconds.

3. **Impact of System Orientation:** We then experimented with tilting the
bottles to different angles. A tilt of approximately 42 degrees provided
the quickest drainage time—2 minutes and 32 seconds. The tilt balanced the
inflow of air and the outflow of water, thereby managing the effects of
surface tension effectively.

4. **Vortex Formation, Symmetry Breaking and the Principle of Least
Action:** In the next step, we swirled the top bottle to form a vortex,
leading to a broken symmetry in angular momentum. This energy-efficient
pathway embodied the principle of least action, allowing the water to
overcome the surface tension barrier and to drain in an impressive 18
seconds. This broken symmetry enabled the efficient dissipation of the
gradient between the bottles.

5. **Effects of Structural Changes:** Our final test involved an open-ended
tube setup. Here, we observed noticeable changes in fluid behavior. The
vortex's efficiency in gradient dissipation decreased due to interference
from the ambient pressure, indicating the crucial role structural features
play in fluid dynamics.

**Conclusion:** The 'tornado in a tube' experiment, complemented by our
additional tests, provided a comprehensive understanding of fluid dynamics
principles. The observed differences in drainage times highlighted the
significant impact of system orientation, the principle of least action,
surface tension, and broken symmetry on fluid dynamics. These findings
offer deeper insights into fluid behavior and are applicable to a range of
real-world phenomena, from weather systems to biological processes.

On Fri, Aug 4, 2023, 8:05 PM Nicholas Thompson <thompnickson2 at gmail.com>
wrote:

> Ok, folks. I apologize to those of you who are fed up with my kitchen
> physics, but there has been a bit of a development in that saga that I want
> to share with those few of you who aren’t.   Years ago, I came home for
> the summer with my ears ringing with the notion that structures are formed
> to dissipate gradients.  Please set aside any teleological implications
> of this statement and ask the question in its most neutral form:  Do the
> structures that sometimes form as a gradient is dissipated dissipate it
> more quickly once the structure has been formed.   Or, as I came to
> interpret it, does facilitating the formation of such a structure speed the
> dissipation of the gradient.
>
> I was the family dishwasher at the time.  I deplore washing dishes, but I
> love messing around with warm soapy water, and so I started to experiment
> with starting the vortex that forms *after* you pull the plug out of the
> sink *before* I pulled the plug.  Quickly, it became apparent that
> facilitating the vortex formation in that way GREATLY SLOWED the emptying
> of the sink.  Triumphally, I wrote Steve on Friam only to be greeted by a
> torrent of scatological raillery, so intense and so persistent from the
> fluid dynamicists on the list that I never heard from Steve. The burden of
> this raillery I have distilled into Roberts Rule of Order:  DEFROCKED
> ENGLISH MAJORS SHOULD NOT BE ALLOWED TO TALK about fluid dynamics.
>
> More than a decade later, I am back in Massachusetts, washing dishes at
> the same sink, and the question occurred to me again. I raised it finally
> with Steve, and he generously sent me the little two-bottle toy, where you
> flip it over and the water drains from one bottle to the other.  As it
> drains, it forms a vortex in the draining bottle, and the occurrence of the
> vortex greatly *increases* the speed of the draining.  Finally, if one
> facilitates the formation of the vortex by rotating the bottle a bit, the
> bottle drains even more quickly.  Thus, the result is entirely different,
> especially if one substitutes two large pop bottles for the ones included
> in the kit.
>
> At the risk of bringing another round of raillery down on my head, I opine
> that the difference has something to do with the fact that two bottle
> situation is more of a closed system than the sink situation.  The test
> would be to saw the bottom off both bottles and demonstrate that
> vortex-formation now slows drainage.
>
> It will be a while, though, before I can get two extra bottles to destroy.
>
>
> Does anybody care to make a prediction and offer an explanation why the
> results should be different in the two cases?
>
> Nick
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