[FRIAM] Swirlies redux

David Eric Smith desmith at santafe.edu
Fri Aug 4 22:38:30 EDT 2023

I think you have several variables in play at the same time here, Nick, and that will make it challenging to get clear what-all is involved, and what is controlling in what combinations.

0. Let me say something general, which won’t be comprehensible within this bullet, but which I will unpack a little in a later one.  I _expect_ that for some fairly symmetric shapes like soda bottles or sinks and drain pipes or whatever, under constant atmospheric conditions etc., water of properties that doesn’t change while it flows (not clear this applies to dishwashing remnant water with soap foams and scums), and so forth, there would be some unique steady state that was the true dynamical state the system would settle into over a sufficiently long time.  The simplest set of questions you could try to ask about would be the properties of that steady state: what it does as a transport process; what boundary conditions it depends on, etc.  What that means is, no bifurcations into several possible, but distinct, indefinitely long-persisting steady flow conditions. Give me that expectation for now, so I can make another point.  Proving when it applies will be some nightmare of going into details, which I probably couldn’t do, certainly don’t have time and patience to try, and probably couldn’t put into English even if I could do it.  From that one question, everything else gets harder because more dimensions come into play.  In particular, there could a whole continuous parameter range of long-lived transients, which decay toward the long-term steady state only very slowly.  Your problem as a dishwasher or bottle tilter is: you may not have as long to wait as it takes those transients to decay.  It’s Keynses “in the long run, we are all dead” (Strictly: that was the point he was making.)

1. So at the least, the fact that you can store the water before pulling the plug, and affect the drain time, means you can put different amounts of angular momentum into the water that cannot get transferred out fully, fast enough to not leave an imprint on the draining.  Since the only way to get down the drain is to first get _to_ the drain, if you put enough angular momentum into the water, it makes it harder for any of it to get to the center.  Why (among other factors) hurricane eyes don’t close.  So indeed, you can stir in a way that gives the water slower access to the drain, and causes it to take longer to all get through it.  

2. There is a different issue of closed versus open.  The reason the soda bottles mouth-to-mouth are so useful is that the only way water can go down is if air goes up.  But the bottles are small enough that for air to bubble up through the water requires getting through enough surface tension that it significantly affects the draining.  Having “enough” vortex to obviate that need then speeds your drainage.  But with the soda bottles too, if you spun them continuously, to keep introducing angular momentum to the water faster than it could transfer away toward the steady state by dissipation, I think it is sure you can affect the drainage.  I suspect the shape of the soda bottles is such that angular momentum equalizes toward the steady state more quickly.  A sink with a flat bottom should be very hard, because you can put in tons of angular momentum that doesn’t get quickly reflected back.  (Also, square or round perimeter and bowl shape of the sink, how full is it relative to width, and other such things.  It can get as complicated as billiards (not really, but figuratively), if you consider all the momentum reflecting around.). 

3. The hard thing to do in emails or posts, and which really will require some computer program in the general case, is to figure out how gravity — in the infinitely long term — interacts with pressure and wall friction to resupply angular momentum to maintain a steady-state vortex, for a given vessel shape, mouth width, etc.  

The question of when you can make a universalizing claim, such as “symmetry breaking (like adding a rotation) will certainly increase or decrease a downward flow”, remains an important one, and many of us have daily instances of that problem in one or another area (ecological dynamics, physiology versus natural selection in populations, and on and on).  So, good to have ongoing interest.  The amount one has to say to have spoken carefully, to figure out what categories are coherent for which to try to generate answers, remains striking (at least to me).


> On Aug 5, 2023, at 11:05 AM, 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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