W. G. Pritchard Lab Seminar: 3:30-4:30 PM, 103 Osmond Laboratory

	          **Monday November 11, 2002**
	
Transition from Ciliary to Flapping Mode in a Swimming Mollusc: 
            a Bifurcation in Reynolds Number 

Stephen Childress

Courant Institute 
New York University

Abstract:

From observations of swimming of the shell-less pteropod mollusc Clione 
antarctica, we compare swimming velocities achieved by the organism using 
ciliated surfaces alone with velocities achieved by the same organism using 
a pair of flapping wings.  Flapping dominates locomotion above a swimming 
Reynolds number Re in the range 5-20.  We test the hypothesis that this 
condition marks the onset of ``flapping flight'' in these organisms.

We consider the proposition that forward / reciprocal flapping flight is 
impossible for organisms whose motion is fully determined by a body length 
L and a frequency W below some finite critical value of the Reynolds number 
given by these parameters.  For a self-similar family of body shapes, the 
critical Reynolds number should depend only upon the geometry of the body 
and the cyclic movement used to locomote.  We give evidence of such a 
critical Reynolds number in our data, and study the bifurcation in several 
simplified theoretical models.

We argue further that this bifurcation marks the departure of natural 
locomotion from the low Reynolds number or Stokesian realm and its entry 
into the high Reynolds number or Eulerian realm.  This occurs because the 
equilibrium swimming or flying speed U obtained at the instability is 
determined by the mechanics of a viscous fluid at a value of a 
corresponding Reynolds number which is not small.