Dynamical characteristics of a higher dimensional model of magnetized Rossby waves in the ionospheric E-layer and modulational instability analysis

Abstract

Rossby waves are important large-scale dynamic wave modes in geophysical fluids. In the ionospheric E-region, magnetized Rossby waves significantly modulate plasma motion through nonlinear coupling with neutral winds and the dynamo process. Thus, they play an important role in the evolution of ionospheric dynamics. This study focuses on the nonlinear dynamic characteristics of magnetized Rossby waves. Using the geomagnetically corrected quasi-geostrophic potential vorticity theory, multi-scale perturbation expansion, and coordinate transformation, we derive the (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation. The Hirota bilinear method is used to solve this equation, obtaining breather-type traveling wave solutions. Rogue wave solutions are further constructed via the homoclinic breather limit method. Modulational instability analysis confirms that the real constant background steady-state solution is linearly stable. Numerical simulations are performed to plot amplitude evolution, two-dimensional distributions, and flow field evolutions of the solutions under different background flows. The influences of the \(\beta \) effect and the geomagnetic latitudinal gradient effect on the flow field evolution of the two solutions are also investigated. Results show that breather-type traveling waves have stable periodic oscillation and directional propagation. Rogue waves exhibit obvious spatiotemporal localization, with sudden amplitude amplification and rapid attenuation. Variations in the \(\beta \) effect and geomagnetic latitudinal gradient effect trigger changes in the generalized Rossby parameter, which substantially modulates the evolution of the two types of wave motions. This study clarifies the nonlinear propagation laws and coherent structure characteristics of magnetized Rossby waves, providing important theoretical support for ionospheric wave dynamics research and space weather prediction.