Francis Poulin

A consistent theory for linear shallow water waves

Francis Poulin
University of Waterloo

In this seminar I will provide a consistent and unified theory for Kelvin, Poincare (inertial-gravity) and Rossby waves in the rotating shallow-water equations. This is based on the original presentation in Paldor et al. (2007) and the corrections of Poulin and Rowe (2008). In particular, I will present a second order boundary value problem which contains all three wave types as well as numerical solutions using an exponentially accurate pseudo-spectral method based on Chebyshev polynomials. The main results of the new theory are that Rossby waves can have larger phase speeds than what is predicted from the classical theory and Rossby and Poincaré waves can be trapped near the southern boundary. I will also present some results of how this approach has been generalized to the linear Boussinesq equations.