The transparency of ocean barriers to Rossby waves: The Rossby slit problem

The transmission of barotropic Rossby wave energy through a meridional barrier pierced only by narrow gaps is studied with a quasigeostrophic model. The incident Rossby wave has the form of either a plane wave or a localized beam of wave energy. The application of Kelvin's theorem on a contour girdling the separated segments of the barrier demonstrate the necessity for wave transmission and helps determine the amplitude of the transmitted wave. When the meridional scale of the incident wave is much larger than the gaps in the barrier, the transmission becomes independent of the gap width. The problem of a barrier with two or three gaps is discussed. In the former case a single bubble of wave energy issues from the region spanned by the separated barrier segment. When a third gap or slit is allowed, the structure of the transmitted wave alters depending on the symmetry of the wave field and the angle of the incidence of the ray trajectory of the incident wave.