Scalar equations as asymptotic models for internal waves in Oceanography

Scalar equations as asymptotic models for internal waves in Oceanography

-
Vincent Duchene , Columbia University
Fine Hall 314

We propose to derive rigorously scalar asymptotic models for the propagation of gravity waves at the interface between two layers of immiscible fluids of different densities (modeling fresh and salt water interface). The KdV equation is known to accurately describe such a system in the long wave regime, but the rigorous justification of this fact is recent. We will present and extend this result to a regime allowing greater nonlinearities, yielding higher order equations, of Camassa-Holm type.