Colloquium
3:00 p.m., Friday (January 28, 2005)
MATX 1100
David Ambrose
Courant Institute, New York University
Analysis and computing for freesurface problems in fluid dynamics
The motion of interfaces in fluids is central to a remarkable number
of natural and engineered systems: some examples are the swimming of fish,
waves on the ocean, and the flow of blood. Fluid interfaces can exert
geometric forces on the surrounding fluid (e.g. surface tension) and can
also have inertial forces (e.g., a heavy membrane). Consequently, the
equations describing their motion are both highly nonlinear and nonlocal,
making both analytical and numerical studies difficult. In this talk,
I will discuss my solution of one such analytical problem, the wellposedness
of vortex sheets with surface tension; this work is heavily influenced by
sophisticated numerical methods developed to evolve such interfaces.
I will discuss an extension of these ideas to both the analysis and
simulation of "inertial interfaces", and discuss how new analysis for
the 3D vortex sheet problem may be suggesting new routes to numerical
simulation.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).
