PHYSICAL MATHEMATICS SEMINAR


TOPIC:	BENDING LEAVES AND FLAPPING FLIGHT:
	TRANSITIONS IN FLOW-BODY INTERACTION PROBLEMS


SPEAKER:	SILAS ALBEN
		Courant Institute of Mathematical Sciences
		New York University

ABSTRACT:

The coupled motion of fluids and solids in contact is common in the
biological world, and leads to unexpected phenomena and new problems 
for theoretical mechanics.  These phenomena can often be understood by
identifying new length and time scales intrinsic to the fully-coupled
system.  I will discuss recent work on two problems in this area, both of
which arose from experiments in the Applied Mathematics Lab at Courant.

The first study concerns the bending of a flexible 2-D body immersed in a
steady planar flow, and is motivated by the flexibility of organic
structures in fluid environments.  In our model we find a transition from
the quadratic growth of drag with flow speed typical of rigid bodies to a
much-reduced 4/3-power law.  We also find that the body and wake assume a
unified, parabolic form.  I present an asymptotic argument which explains
the governing phenomenon: the formation of a "tip region" on the fiber,
which gives rise to global self-similarity.

In the second problem, I study a fluid flow problem at the transition
between low- to high-Reynolds-number locomotion.  A 2-D rigid wing is
flapped in the vertical direction and is free to move horizontally.
Above a critical flapping speed, it has been shown experimentally and in
my numerical study that the wing becomes unstable to horizontal motion.
I will explore the intriguing coupled dynamics in the neighborhood of this
critical speed, in which the nondimensional body mass plays an important
role.  This problem was originally inspired by the swimming strategies of
small molluscs, but generally improves our understanding of the generation
of thrust in flapping flight.


DATE:		TUESDAY, FEBRUARY 10, 2004
TIME:		2:30 PM
LOCATION:	Building 2, Room 338

Refreshments will be served at 3:30 PM in Room 2-349

Massachusetts Institute of Technology, Department of Mathematics
Cambridge, MA  02139