Energy Transmission by Barotropic Rossby Waves Revisited

Abstract

Abstract This article presents a semianalytic method to investigate the properties of energy transmission across bottom topography by barotropic Rossby waves. The method is first used to revisit the analytical estimates derived from wave-matching techniques and Wentzel–Kramers–Brillouin (WKB) approximations. The comparison between the semianalytic method and WKB indicates that the results of the latter are valid for waves with periods longer than a month and ridges taller than ∼1000 m and wider than ∼500 km. For these parameter values both methods predict the passage of low-frequency waves and the reflection of high-frequency waves. The semianalytic method is then used to discuss the energy transmission properties of a cross section of the Mid-Atlantic Ridge. It is shown that the filtering characteristics of realistic bottom topographies depend not only on the spatial scale set by the cross-section envelope, but also on the scales of the individual peaks. This dependence is related to the fact that topographies narrower than ∼400 km (e.g., peaks) are high-pass filters of incoming waves, while topographies wider than that (e.g., cross-section envelopes) are low-pass filters. In the particular case of the Mid-Atlantic Ridge the neglect of the contribution of individual peaks leads to an erroneous estimate of the filtering properties of the massif.