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Shape Optimization of Swimming Sheets
Applied Math| Speaker: | Jon Wilkening, University of California, Berkeley |
| Location: | 1147 MSB |
| Start time: | Fri, May 26 2006, 4:10PM |
Description
The swimming behavior of a sheet which moves via wave propagation was
first studied by G. I. Taylor in 1951. In addition to being of
theoretical interest, this problem serves as a useful model of the
locomotion of various micro-organisms and a few larger animals such as
snails. We show how the shape of the wave affects the swimming speed
and power required to swim, and present numerical techniques to find
the fastest and most efficient swimming strategies when arclength and
fluid volume are constrained. For each optimization problem, we
obtain a one parameter family of solutions that become singular in a
self-similar fashion as the parameter approaches a critical value. We
explore the validity of the lubrication approximation used to model
the dynamics by monitoring higher order corrections to the zeroth
order theory. These corrections are themselves validated by
comparison with finite element solutions of the full Stokes equations.