Nonlinear Systems Group                                 University of Illinois at Urbana-Champaign

Director: N. Sri. Namachchivaya 306 Talbot Laboratory, 104 South Wright Street Urbana, IL 61801 Phone: (217) 244-0683, Fax: (217) 244-0720 E-mail: navam@uiuc.edu Department of Aerospace Engineering Created: 11/16/2003 Last Updated: 11/16/2003			Surface waves   Waves can form at the surface of water contained in a cylindrical vessel by shaking the vessel. Ignoring second-order effects (eg. compressibility, surface tension, viscosity) this fluid dynamical system can be described by a Hamiltonian, with gravity acting as a restoring force. When the two dominant surface wave modes are near 1:1 resonance, the system evolves on a three-leaved graph. Using stochastic averaging, it becomes possible to calculate probability density functions for wave modes that are generated by stochastic shaking. The results of this investigation may provide insight into problems ranging from the capsizing of ocean-going ships to microgravity experiments performed in outer space.