Florida State University Seal

Catherine Sulem


Speaker: Catherine Sulem
Title: Water Waves Over a Rough Bottom in the Shallow Water Regime
Affiliation: University of Toronto
Date: Friday, March 25, 2011
Place and Time: Room 101, Love Building, 3:35-4:30 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. I will present a study of the Euler equations in two and three dimensions for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem of homogenization theory. In this setting we derive a new model system of equations, consisting of the classical shallow water equations coupled with nonlocal evolution equations for a periodic corrector term.

Solutions of the latter can exhibit the effect of Bragg resonance with the periodic bottom, which leads to secular growth and can influence the time interval of validity of the theory. We justify the derivation of the model with an analysis of the scaling limit and the resulting error terms.

This is a joint work with Walter Craig and David Lannes.