Category: Hydrodynamics

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Solitons

We only address linear media in introductory physics classes, and really only focus on infinite or semi-infinite sine-wave-like disturbances.  In the real world waves have a finite duration; this type of wave is often called a wave packet.  If the wave is large enough, it can be affected by the nonlinear properties of the medium.  The most dramatic example of this is the soliton, a disturbance that propagates with no loss in speed, size or shape over large distances.

Though first observed more than 150 years ago, solitons weren’t understood until the last few decades and are still actively investigated in mathematics, physics and engineering.  This site gives an overview of current research as well as a historical account of the first description of a soliton on a canal in England.

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Swimming in goop

Chemical engineers at the University of Minnesota filled a swimming pool with guar gum (which should be familiar to anyone who reads food labels) to answer the age-old question “Can you swim faster in goop than in water?”

High Reynolds number hydrodynamics (roughly speaking, the study of large, fast things in water, where Re>1) is considerably more complex than low Reynolds number hydrodynamics (roughly speaking, the study of small, slow things in goop, where Re<1).  Since a swimming human operates in the complicated high Reynolds number regime (at Re ~ 4.5 × 106), there had been controversy about whether people would swim more or less quickly in viscous goop.

Short answer: it makes no difference whatsoever.  But lest you feel disappointed, this research did earn Cussler and Gettelfinger one of the highest-profile prizes in the natural sciences: an Ig Nobel!  Unfortunately, their goop only increased the swimming pool’s viscosity by a factor of two, which means that all else being equal (and, in fact, all else was equal because their test subjects swam at exactly the same speed as in water) the Reynolds number was only 2× smaller in the goop.  This is still very far from the simple yet weird physics that occurs at small Reynolds numbers.

The Great Molasses Disaster. Caused by deregulation of the molasses industry, no doubt.

Cautionary note: this experiment is sometimes incorrectly compared to swimming in molasses.  This is a dangerously bad analogy.  You can swim in a swimming pool filled with guar gum goop, but you cannot swim in molasses.  In fact, molasses are very dangerous.

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Tsunamis

A tsunami is an unusually large wave triggered by a major force (usually an earthquake) applied to the ocean.  In the open ocean a tsunami does not have a particularly large amplitude, but its wavelength is enormous.   As it approaches land, the amplitude of a tsunami can increase dramatically, leading to catastrophic flooding.

Several sites, some more media-rich than others, present conclusion about the physics of tsunamis.  The origin of tsunamis is well understood (though, because most are caused by earthquakes, impossible to predict).  Any short, sharp excitation of sufficient size can cause a tsunami; as in many wave-bearing media, the specific details of the excitation are not as important as its total size.

My reconstruction of the major practical difficulties in tsunami warning is

  1. Since the tsunami has a small amplitude in the open ocean, it is difficult to detect before it nears shore, and
  2. Whether a small amplitude open-ocean tsunami turns into a large amplitude wave near shore (called “shoaling”) depends critically on the details of the shoreline and the direction of approach of the wave.  During the time between the triggering of a wave and its arrival on land, there is often not enough information to precisely calculate the threat to populated areas and then to communicate an appropriate warning.  After the fact it is possible to reconstruct the path of the wave, but this is small consolation to the survivors.
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Quicksand

Obviously, most people study hydrodynamics for its many practical benefits in everyday life, viz., understanding shear-thinning colloidal fluids allows one to escape quicksand.

While a popular treatment of the phenomenon should keep most of my readers safe, it lacks many technical details found in the literature.   Most quicksand is not lethal if dealt with correctly, but some researchers are less optimistic about the possibility of survival.

I particularly recommend this literature to students majoring in physics.  Should one of you die a slow, agonizing quicksand-induced death, you would have only yourself (or, more precisely, your ignorance of the rheology of saturated granular beds) to blame.  This would be particularly embarassing for the dual geology / physics major, who is not unlikely to encounter such perilous situations during field work.

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Swimming: high vs low Reynolds number

The Reynolds number (Re) is a dimensionless quantity that describes whether inertial effects (such as coasting) are important during propulsion in a fluid.  The mathematical description of fluid flow predicts that certain kinds of motion that work perfectly well for high Reynolds number propulsion completely fail at low Reynolds number.  In particular, reciprocal (back-and-forth) motions work for Re>1 but not for Re<1.

The Reynolds number of flow around an object is Re = vd?/?, where v is the speed of the object, d is the size of the object, ? is the density of the fluid and ? is the viscosity of the fluid.  The easiest way to observe the effect of Reynolds number is to move an object from swimming in a tank of water (?~1 cP) to swimming in a tank of corn syrup (?~2000 cP) or silicone oil (? as high as 100,000 cP).  This reduces the Reynolds number of the motion by at least a factor of 2,000 to 100,000.

[youtube]http://www.youtube.com/watch?v=4h079P7qRSw[/youtube]

A classic example of this is a rigid flapping arm or oar.  It propels at high Re, but not at low Re.

[youtube]http://www.youtube.com/watch?v=2kkfHj3LHeE[/youtube]

Since a simple reciprocal motion won’t propel an object at Re<1, the motion needs to be more complicated.  Instead of a back-and-forth motion, bacteria continuously turn a helical flagellum to propel themselves.  As demonstrated by this helical propeller model, this strategy does work at low Re.

[youtube]http://www.youtube.com/watch?v=s_5ygWhcxKk[/youtube]

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Shear-thickening fluid

[youtube]http://www.youtube.com/watch?v=f2XQ97XHjVw[/youtube]

Cornstarch is famous as a shear-thickening fluid, leading to both sober and amusing experiments.  If you were trying to transport a block that continuously excreted a thin layer of cornstarch, the harder you pulled it the more frictional force you would feel.  Snails use the exact opposite strategy: they excrete a shear-thinning fluid that allows them to move even though they’re never actually in direct contact with the ground.

Shear-thickening fluids are also used in prototype bulletproof fabrics.

The normal model of friction at an interface posits that static friction perfectly counteracts any force applied to an object, up to the maximum value fsmax= µs N; then friction jumps to the smaller value  fk= µk N and remains constant as long as the object is moving.  This is equivalent to saying that the interface acts like an infinitely strong shear-thickening film up to the yield force of µs N,  instantly shear thins to µk N and thereafter is shear neutral.  This analogy is imperfect, however, because the behavior of a real shear-thinning or -thickening fluid depends strongly on its depth, while there is no equivalent idea of the depth associated with µs and µk.

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Plane on a conveyor belt

Can a plane taxiing on a backward-moving conveyor belt take off?  This would seem to be a standard artificial end-of-chapter physics problem, but it escaped to the internet and became a controversy.  To those who understand about relative velocity (and who know that thrust is generated by the air moved by a plane’s jet or prop), the answer is pretty straightforward, but you can check out the Mythbusters test (parts one and two) to make sure.

On further reflection, perhaps “straightforward” is overly optimistic.  But you should be able to see why a real plane can take off, even taxiing against a moving conveyor, and how the question generated so much froth on the intertubes due to its ambiguous wording.