The domain of validity of the KdV-type solitary rossby waves in the shallow water β-plane model

Abstract

Abstract The Domain, where the necessary and sufficient conditions for the existence of the KdV-type solitary Rossby waves are satisfied is defined in the shallow water β-plane model. The KdV-type solitary Rossby waves are the Rossby waves whose time-longitude dependence is determined by the KdV equation. As far as an appropriate amplitude and an appropriate ratio of the scales of the east-west and north-south directions are given, the KdV-type solitary Rossby waves can exist for every basic zonal flow. This result suggests the large validity of the soliton model in geophysical fluid dynamics. The KdV-type solitary Rossby waves are classified into four categories: (1) shear solitons studied by Long, Larsen, Benny, Redekop, and Hukuda, (2) β-divergent solitons studied by Clarke, Yamagata, and Nogami, (3) β-solitons found in the case of the strong stratification, and (4) divergent solitons which exist in the planetary-geostrophic-scale zonal flow. A remarkable result is that, in addition to the conventional east-west elongated solitons, the north-south elongated solitons can also exist for the case of the divergent solitons.