The control model of Rossby waves and dynamic characteristics in stratified fluids

Na Cao, XuHai Li and XiaoJun Yin

Chaos, Solitons & Fractals, 2025, vol. 201, issue P1

Abstract: This paper investigates the dynamical model of nonlinear Rossby waves in stratified fluids. We derived one forced nonlinear Boussinesq equation from the quasi-geostrophic barotropic potential vorticity equation incorporating dissipation, topography and external heat sources to describe the evolution and development of nonlinear Rossby wave amplitude. This study developed an innovative method that combines bilinear neural networks with symbolic computation, bypassing the traditional requirements of bilinear formulas and achieving more efficient solution of NPDEs. We presented the neural network architectures for both single-layer and multi-layer exact solutions, and based on these structures, we derived the lump solutions, lump-soliton interaction solutions, and exact solutions under a two-layer neural network framework for the forced nonlinear Boussinesq equation. A key finding is that the stratification effect α4 significantly influences the amplitude and propagation direction of nonlinear Rossby waves, the wave amplitude will increase as α4 intensifies. These results comprehensively reveal the crucial role of stratification effects on Rossby wave dynamics.

Keywords: Boussinesq equation; Stratification; Neural network; Multi-layer exact solutions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012214

DOI: 10.1016/j.chaos.2025.117208

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