The Zakharov-Kuznetsov Equation as a Two-Dimensional Model for Nonlinear Rossby Waves

2003/12/04 by Georg A. Gottwald, Gottwald, Georg A. · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Meteorological Phenomena and Simulations #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Pattern Formation and Solitons (nlin.PS) #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0312009

12 pages

arxiv created 2003/12/04 · openalex publication_date 2003/12/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of two-dimensional coherent structures in planetary atmospheres and oceans. We derive the Zakharov-Kuznetsov equation for large scale motion from the barotropic quasigeostrophic equation in a weakly nonlinear, long wave approximation. We consider coherent structures emerging out of an instability caused by a narrow jet-like meanflow. We use multiple scale analysis combined with asymptotic matching.

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