Three types of generalized Kadomtsev–Petviashvili equations arising from baroclinic potential vorticity equation

In this article, the variable coefficient (2 + 1)-dimensional extended cylindrical Kadomtsev–Petviashvili (cKP) equation describing Rossby waves was derived from the quasi-geostrophic potential vorticity equation. It is difficult for the variable coefficient cKP equation with dissipation to calculate the exact solution. For obtaining the exact solution, a new transformation was constructed for the first time to reduce the extended cKP equation to the extended KP equation. We emphasize that the exact solution, and not just approximate solution, in Rossby waves flow field can be obtained when dissipation is included. The exact lump and interaction solutions with dissipative effect are given according to the modified Hirota bilinear method, and physics for the evolution of Rossby waves is analyzed based on the obtained solutions. When the dissipative parameter μ0 increases, the structure of the amplitude A changes in the spatial scale y. And when the dissipative parameter increases to a certain value, the structure of Rossby waves tends to be stable. It is pointed out that the dissipative parameter μ0 determines not only the amplitude A of Rossby waves but also structures of Rossby waves flow field, with μ0 acting on the spatial scale y and the timescale t.

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Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

Yin,

Du,

Wang

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Starting from the classical quasi-geostrophic potential vorticity equation with equal depth two-layer fluid, the coupled cylindrical Kadomtsev–Petviashvili (KP) equations with variable coefficients for Rossby waves are studied. To be more general, the phase velocity is considered an indefinite integral about time and improves the analysis procedure. So the variable coefficients are obtained and some previous studies are reasonably explained. The cylindrical wave theory is therewith utilized to reduce the coupled cylindrical KP equations with variable coefficients, and based on the modified Hirota bilinear method, the lump solutions and interaction solutions are found. Through numerical simulations, the Rossby lump waves on both sides of the y axis move closer to the center, and their amplitude gradually decreases and tends to flatten with the generalized Rossby parameter growth. In the Rossby waves flow field, the dipole structures propagate to the east and lead to the appearance of the compress phenomenon during barotropic–baroclinic interaction. It is possibly useful for further theoretical research on atmospheric phenomena.

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Three types of generalized Kadomtsev–Petviashvili equations arising from baroclinic potential vorticity equation

Abstract: Zhang Huan-Ping(张焕萍) a) , Li Biao(李彪) a)d) † , Chen Yong (陈勇) a)b) , and Huang Fei(黄菲) c)

Cited by 8 publications

References 20 publications

Variable coefficient (2+1)D KP equation for Rossby waves and its dynamical analysis

Variable coefficient (2+1)D KP equation for Rossby waves and its dynamical analysis

Variable coefficient extended cKP equation for Rossby waves and its exact solution with dissipation

Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

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Three types of generalized Kadomtsev–Petviashvili equations arising from baroclinic potential vorticity equation

Abstract: Zhang Huan-Ping(张焕萍) a) , Li Biao(李 彪) a)d) † , Chen Yong (陈 勇) a)b) , and Huang Fei(黄 菲) c)

Cited by 8 publications

References 20 publications

Variable coefficient (2+1)D KP equation for Rossby waves and its dynamical analysis

Variable coefficient (2+1)D KP equation for Rossby waves and its dynamical analysis

Variable coefficient extended cKP equation for Rossby waves and its exact solution with dissipation

Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

Contact Info

Product

Resources

About

Abstract: Zhang Huan-Ping(张焕萍) a) , Li Biao(李彪) a)d) † , Chen Yong (陈勇) a)b) , and Huang Fei(黄菲) c)