How does moving your legs propel you forward in swimming?

  • #26
marcusl
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Purcell's paper is not directly relevant here because bacteria swim at *very* low Reynolds numbers where our experience fails to apply. Purcell states that a swimming bacterium is equivalent to a human sitting in a swimming pool of molasses and moving no part of his/her body more rapidly than 1 cm/minute! As just one difference, micro-organisms do not generate the vortices that are an important part of how we swim. Having said that, it is a remarkable paper.
 
  • #27
Andy Resnick
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<snip> As just one difference, micro-organisms do not generate the vortices that are an important part of how we swim.
Wrongedy-wrong. See flagellar locomotion and nematode swimming. Gray and Hancock's 1955 paper has some nice detail. And again, Lighthill's book is comprehensive.

Unless you mean that having arms and legs makes human swimming radically distinct from other forms of aquatic locomotion.
 
  • #28
marcusl
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I'm speaking of vortices in the fluid, not rotational motion of a flagellum. At the low Reynolds numbers that Purcell considers, inertia effects are negligible compared to viscous effects (he points out that inertial forces die away in distance of order 0.1 Angstrom!). How are vortex rings sustained in that regime?
 
  • #29
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How are vortex rings sustained in that regime?
I'm kind of lost, but wouldn't a vortex waste more energy while it is spreading out... while the ring contains itself far more efficiently?
 
  • #30
marcusl
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The issue I raised is only that Purcell's paper does not describe human swimming but rather that of bacteria for whom inertial forces in the fluid are negligible. I believe in that case that the fluid cannot support vortices of the sort you described for human swimming and that have been observed shedding off of the tails of fish.
 
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  • #31
Andy Resnick
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I'm speaking of vortices in the fluid, not rotational motion of a flagellum. At the low Reynolds numbers that Purcell considers, inertia effects are negligible compared to viscous effects (he points out that inertial forces die away in distance of order 0.1 Angstrom!). How are vortex rings sustained in that regime?
As I mentioned, Purcells' paper is a *starting* point, kind of like how frictionless surfaces and massless pulleys are used in introductory mechanics. Since you (apparently) don't have access to Lighthill:

http://maeresearch.ucsd.edu/~elauga/research/references/LaugaPowers09_RPP.pdf

and
http://www.pnas.org/content/early/2011/07/28/1106904108.full.pdf

Figure 8 of #2 is instructive, as vortices are clearly present. In the fluid. More than 0.1 Angstrom away.
 
  • #32
marcusl
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Thank you, I will read these.
 

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