It is my pleasure to offer an explanation. My discipine area is actually structural mechanics and dynamics, but I do occasionally perform analysis of fluid-structural interactions (with the aid of a CFD analyst) and have a working knowledge of fluid mechanics. No real world fluid dynamic problem is ever as simple as the trivial explanations provided in basic physics classes would suggest.
Although it is not directly peritnent to the original question, the Flying Circus of Physics website has this discussion about hydraulic jumping from faucets.
Is there a CliffNotes version of the straightforward explanation? But thank you muchly for avoiding the difficult explanation with non-linear PDE’s.
Can I try a very simple intuitive explanation? Imagine, oversimplifying, a cylindrical shape of water above the drain falling straight down. The surrounding water will need to rush in and fill the voiding cylinder. But if you try to visualize what trajectory that incoming water would need to take – you fail! There’s a mismatch in position and/or volume. Filling the voiding cylinder with a swirling-in addresses this mismatch. (Similar swirling, also stochastic, arises in Rayleigh–Bénard convection.)
(I’m sure Stranger’s explanation is correct. Whether mine is, vaguely, correct or related to Stranger’s is left as an exercise.)
To me, the aspect which Stranger explained so well, and which I think you just now failed to emphasize, is that it is SMALL, random turbulent movements which then coalesce into a more coherent, larger swirl in one direction (typically), as those small bits of water “capture” other bits around them, and more of these enlarging regions happen to be going in one direction than in the other, until very soon the whole thing is going in that direction. The conga line, in other words. (Also, clapping among European jazz audiences.) I assume that it is due to the “stickiness” of water molecules – how each molecule is, to a degree, “stuck” to it’s neighbors – that allows these small bits of water to “influence” the bits around them in this way.
To me, the cool thing is that you can observe this all happening in your bathtub! The initial chaos, the coalescing of regions, the emerging dominant flow in one direction or the other, the differential speeds based on distance from the outlet throughout the process…
This coalescence of random influences into predictable systematic behavior–known as emergence–can be seen in many physical phenomenon that would otherwise seem to be planned or guided by some off-stage actor. However, despite my use of a virtual particle for visualiation, my above description stops at the level of continuum mechanics, i.e. it treats the water as a continuous medium without consideration for the behavior on the molecular level, which would require delving into the electrodynamics of intermolecular forces. Water is slightly polar (which contributes to the surface tension and cohesive properties) and its molecular properties do affect how it interacts with itself and other substances, but for the purposes at this level we only need be concerned with the density and viscosity. Given the same conditions, a more viscous fluid, like mineral oil, will end to damp out the turbulence, while a less viscous fluid, like liquid hydrogen, may flow so easily that turbulence occurs readily but does not dominate the overall flow and it has to be pressurized to get it to mix properly. Generally speaking, when modeling fluid behavior, we do not get down to modeling the molecular behavior except in chemically active fluids (e.g. those undergoing combustion or decomposition) or in very rareified gaseous phases, where a very computationally intensive stochastic method called direct simulation Monte Carlo (DSMC) is used to estimate aggregate fluid behavior.
Indeed. When you start looking at the world in detail, you see that even the most simple phenomena are actually the result of very complex interactions at levels below what we can easily observe. Science, in the modern sense, began out of a desire to classify the nature into simple, discrete phenomena, but has ended up giving us a dramatically more nuanced view of the inherent interrelationships between seemingly separate mechanisms. Far Keat’s light-hearted complaint Newton’s “unweaving the rainbow”, an examination of nature at more fundamental levels gives us an understanding of the intricate and beautiful complexity of nature.
OK. I’ll admit to a bit of bad tempered snark. After the prior excellent post describing in exceptional detail the mechanics of the swirl and how the Corolis force is not needed to account for it, to trot out that old warhorse without acknowledging any other post in the thread just pushed my buttons.
This is the Cliff notes version to me. Of course more research is needed on how conga line direction is initially determined and the effect of water molecules wearing lampshades as hats. Science marches forward.
