Nonlinear planetary-synoptic wave interaction under generalized beta effect and its solutions.

• An nonlinear Schrödinger equation is obtained in simulating the evolution of planetary Rossby solitary waves while considering the generalized β (y). • Generalized β (y) is denoted to modify the linear phase speed and growth/decay characteristic of the planetary scale solitary wave packet. And asymmetry, intensity and persistence of each kind of flow fields depend strongly upon β (y). • The generalized β (y) and weak shear background current are found to share qualitative similarity in influencing the evolution of Rossby solitary wave packet. The interaction between planetary-scale wave and synoptic-scale wave in atmospheres is important in understanding the physical mechanism of short or long term weather or climate events, such as the blocking phenomena. Kinds of physical factors are disclosed to affect the interaction processes, such as the topography, background current. The effect of beta parameter is investigated in the present paper, it is called the generalized beta effect. By using methods of multiple scales and perturbation expansions, a new nonlinear forced Schrödinger equation is obtained in describing the evolution of planetary-scale envelope Rossby solitary waves, and a modified equation for synoptic-scale waves is derived. By constructing the numerical solution for the nonlinear Schrödinger equation, it reveals that the generalized beta can shift phase and modify the magnitude of planetary-scale envelope solitary waves. An analytical expression for synoptic-scale waves, including the generalized beta effect, is also obtained. It shows that the asymmetry, intensity and persistence of both planetary-scale wave and synoptic-scale wave depend strongly upon the generalized beta. The results provide new theoretical explanations for our understanding of wave-wave interaction. [ABSTRACT FROM AUTHOR]