Energy transmission by barotropic Rossby waves revisited

Abstract

This article presents a semianalytic method to investigate the propertie s of energy transmission across bottom topography by barotropic Rossby waves. The method is first used to r evisit 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 res ults 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 energ y transmission properties of a cross section of the Mid-Atlantic Ridge. It is shown that the filtering cha racteristics 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 topogr aphies narrower than 400 km (e.g., peaks) are high-pass filters of incoming waves, while topographie s wider than that (e.g., cross-section envelopes) are low-pass filters. In the particular case of the Mid-Atlant ic Ridge the neglect of the contri- bution of individual peaks leads to an erroneous estimate of the filtering properties of the massif.