Rossby wave patterns in zonal and meridional winds

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.