Topographic Factor and Limit Transitions in the Equations for Subinertial Waves

In this paper, sub-inertial waves propagating on the Kuril shelf and the oceanic trench are considered. Against the background of a historical review of the beginning of the study of topographic waves and the appearance of relevant terms, a description of the features of wave propagation and the derivation of the main dispersion equations are given. We show that all variants of the topographic solutions presented in the article are basically based on the same dispersion relation: this is the dispersion relation for Rossby topographic waves. Two separate classes of localized solutions have been constructed: one is for the shelf, and the second, in fact, is also for the shelf, but which is commonly called trench waves. We demonstrate that the transverse wave number for trench waves is not independent, as for shelf waves, but is a function of the longitudinal wave number. In other words, Rossby topographic waves are two–dimensional waves, while shelf waves are quasi-one-dimensional solutions. The analytical novelty of the work consists of the fact that we can make crosslinking of trench and shelf waves. This fact was not presented in previous articles on this topic.