Stochastic Confinement of Rossby Waves by Fluctuating Eastward Flows

Adam Hugh Monahan, Lionel Pandolfo, and Peter Imkeller

The effect of stochastic fluctuations in the background zonal velocity field on the energy dispersion of stationary wave responses to meridionally localised forcing is considered, using the non-divergent, barotropic vorticity equation. It is found that for small noise levels or large lengthscales in the noise autocovariance function, the oscillatory structure of the solutions is not altered. However, for noise levels (or autocovariance lengthscales) comparable to or larger (smaller) than those observed in the circulation at 300mb, the marginal density functions of the solution process displays a pronounced attenuation away from the stationary wave source. This indicates that fluctuations in the velocity field inhibit the dispersion of wave energy. The symmetry of the marginal PDFs about the source rather than about the equator indicates that the localisation is primarily an integrated effect of backscattering by potential vorticity gradients in regions of real refractive index, and not due to attenuation by regions of imaginary refractive index or by critical lines in the flow.

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