-----------------------------------------------------------

Applied Mathematics Colloquium

Friday, December 2,  2005, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Small waves, large vortices, and the gait of the water strider

Oliver Buhler

Courant Institute of Mathematical Sciences

New York University

New York, NY

Abstract

The refraction of small-scale waves by large-scale flows is a well- studied problem in mathematical fluid dynamics and it leads to the familiar ray-tracing equations, which describe phenomena such as the wave patterns and currents on beaches and the occurrence of critical layers and clear-air turbulence in the atmosphere. This talk will describe the standard theory and then present new results in this area that are important for understanding the nonlinear interactions between refracted dispersive waves and multi-dimensional mean flows, especially in the atmosphere. In addition, related work is presented on the locomotion of the water strider, which is a small insect that creates both waves and vortices as it moves along the water surface. A new theory suggests that the recoil momentum of the insect is taken up by the waves and vortices with share 1/3 and 2/3, respectively.