The interaction of equatorial waves with a barotro

Authors: Maryam Namazi Boualem Khouider

Publish Date: 2012/01/24

Volume: 27, Issue: 1-2, Pages: 149-176

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Abstract

We compare the performances of two different numerical methods to solve the equatorial shallow water equations in a background meridional shear A coarseresolution Galerkintruncationbased method and a finitevolume method for the case of an equatorial Rossby wave In the presence of the barotropic shear the Rossby wave quickly loses its energy through shear interaction and excites other equatorially trapped waves despite the fact that the PDE system is linear The two methods handle this sudden energy exchange across scales very differently While the finite volume converges statistically to a coherent largescale solution the Galerkin truncation method results in largescale and slow oscillations where energy is bumped back and forth within the resolvedscale spectrum involving higherorder equatorial wave modes heavily depending on numerical resolution that is the number of Galerkin basis functions The addition of an artificial viscosity for the coarseresolution Galerkin method heavily damps the energy oscillations without significantly changing its transient dynamics This provides an example of interaction across scales where the resolution of scales that are apparently not representative of the statistical solution are important for the transient dynamics Therefore nonlinear interactions of equatorially trapped waves may provide an interesting test bed for the validation of climate model dynamical cores

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