Asymptotics of waves on the shallow water generated by spatially-localized sources and trapped by underwater ridges

Abstract

We consider a set of examples describing the behavior of linear nonstationary waves on the shallow water generated by time-instantaneous spatially-localized sources and propagating over underwater banks and ridges. To this end, we use an asymptotic approach developed by the authors of the present paper and their collaborators. The approach uses the generalized Maslov canonical operator. We establish the occurrence and dynamics of wave trains travelling over underwater ridges (which are nonstationary waves trapped by ridges) with wave-front singularities, moving focal (turning) points, cascades of space-time caustics, etc.