Trapped Waves: Theory, Simulations and Observations

Nathan Paldor

Hebrew University of Jerusalem

Wednesday, May 30, 2018, 2:00 pm
DSRC Room 1D403

Abstract

In the traditional wave theory of Geophysical fluid Dynamics on the mid-latitude f/β-plane the meridional amplitude structure of Inertia-Gravity (AK A Poincaré) waves and Planetary (AKA Rossby) waves is described by Harmonic functions (e.g. sin(ly+θ) where l is the wavenumber and θ is an arbitrary phase). On the β-plane this result is surprising since the Coriolis parameter, which is one of the coefficient s of the differential system, is y-dependent i.e. f(y)= f₀+βy. In my talk I will formulate a Schrödinger eigenvalue equation that applies to Inertia -Gravity and Planetary waves and solve this equation to derive new explicit expressions for the dispersion relations and meridional amplitude structure of the two waves. In addition, the formulation also underscores the highly degenerate nature of Kelvin waves and it reproduces the equatorial wave theory as a particular case of the mid-latitude waves obtained by setting f₀=0. The analytic results, including the channel width above which Trapped waves control the dynamics, are validated by numerical simulation of the Rotating Shallow Water Equations in a zonal channel on the β-plane. Trapped Rossby waves are shown to describe altimetric observations of westward propagating Sea Surface Height features in the Indian Ocean where the south coast of Australia serves as the required zonal boundary where the boundary conditions are applied.