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Dynamics of Rossby wave packets with topographic features via derivative expansion approach

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Abstract

The derivative expansion method was successfully proposed by scholars to characterize the propagation and to discuss the dynamics of nonlinear water waves in the last century. The results manifest the great superiority of this method. The present paper aims mainly at the uses of this technical method to describe the evolutionary processes and to explain the dynamical mechanisms of nonlinear Rossby waves for large-scale geophysical fluid motions. We derive a nonlinear Schrödinger equation from describing the evolution of Rossby wave amplitude. Furthermore, the boundary value problem is handled by using the perturbation expansion method. The effects of initial amplitude, frequency and zonal wave number on the amplitude of Rossby solitary waves are analyzed in both the presence and the absence of topography cases. The effects of weak shear current on dipole blocking are discussed in the presence of bottom topographic structures. The results indicate that topography has a significant impact on the size of amplitude and propagation speed of Rossby waves, and sheared background current will benefit the generation of blockings.

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Funding

This research was funded by project supported by the National Natural Science Foundation of China (Nos. 12102205 and 12262025), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (No. NJYT23098), the Scientific Startin and the Innovative Research Team in Universities of Inner Mongolia Autonomous Region of China (No. NMGIRT2208).

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  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Zhihui Zhang, Ruigang Zhang, Jie Wang & Liangui Yang

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  1. Zhihui Zhang
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  2. Ruigang Zhang
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Correspondence to Ruigang Zhang.

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Zhang, Z., Zhang, R., Wang, J. et al. Dynamics of Rossby wave packets with topographic features via derivative expansion approach. Nonlinear Dyn 111, 17483–17497 (2023). https://doi.org/10.1007/s11071-023-08775-2

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