Rossby wave patterns in zonal and meridional winds |
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Authors: | CT Duba TB Doyle JF McKenzie |
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Institution: | 1. Department of Mathematics Statistics and Physics, Durban University of Technology, P.O. Box 1334, Durban 4001, South Africa.;2. iThemba Laboratory for Accelerator Based Sciences, Somerset West 7129, South Africa.;3. School of Chemistry and Physics, University of KwaZulu-Natal, Westville, South Africa. |
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Abstract: | The propagation properties of Rossby waves in zonal and meridional winds are analyzed using the local dispersion relation in its wave number form, the geometry of which plays a crucial role in illuminating radiation patterns and ray trajectories. In the presence of a wind/current, the classical Rossby wave number curve, an offset circle, is distorted by the Doppler shift in frequency and a new branch, consisting of a blocking line with an eastward facing indentation, arises from waves convected with or against the flow. The radiation patterns generated by a time harmonic compact source in the laboratory frame are calculated using the method of stationary phase and are illustrated through a series of figures given by the reciprocal polars to the various types of wave number curves. We believe these results are new. Some of these wave patterns are reminiscent of a “reversed” ship wave pattern in which cusps (caustics) arise from the points of inflection of the wave number curves; whilst others bear a resemblance to the parabolic like curves characteristic of the capillary wave pattern formed around an obstacle in a stream. The Rossby stationary wave in a westerly is similar to the gravity wave pattern in a wind, whereas its counterpart in a meridional wind exhibits caustics, again arising from points of inflection in the wavenumber curve. |
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Keywords: | Rossby waves β-plane Radiation pattern |
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