From Sea Waves off the Venice coast to Traveling Waves in Navier-Stokes Equations

Applied and Computational Mathematics Seminar
Monday, March 11, 2013 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Georgia Tech, Civil & Environmental Engineering
I will present some results on the space-time stereo reconstruction of nonlinear sea waves off the Venice coast using a Variational Wave Acquisition Stereo System (VWASS). Energy wave spectra, wave dispersion and nonlinearities are then discussed. The delicate balance of dispersion and nonlinearities may yield the formation of solitons or traveling waves. These are introduced in the context of the Euler equations and the associatedthird order compact Zakharov equation. Traveling waves exist also in the axisymmetric Navier-Stokes equations. Indeed, it will be shown that the NS equations can be reduced to generalized Camassa-Holm equations that support smooth solitons and peakons.