Collision Interactions of Envelope Rossby Solitons in a Barotropic Atmosphere

Abstract

A theory is developed here to describe the propagation of nonlinear Rossby wave packets in a barotropic atmospheric model and their interactions by using the multiple-scale method. It is shown that the propagation of a single Rossby wave packet can be described by the nonlinear Schrödinger equation that has envelope soliton solutions. For two interacting packets with slightly different wavenumbers they satisfy a set of two coupled nonlinear Schrödinger equations. These equations are used to study the collision interactions of two envelope Rossby solitons. It is found that despite the complexity of the interaction, the energy of each soliton is conserved, while the shapes and velocities of the two solitons may be altered significantly by the interaction. The action of one soliton on another is realized by providing a field of force or potential for it through the cross-modulation terms.