Francis Poulin
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A consistent theory for linear shallow water waves

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Francis Poulin

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University of Waterloo
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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.