Abstract
A new three dimensional nonlinear dynamic theoretical model is derived from fluid mechanics system. In this paper, From the quasi-geostrophic barotropic potential vorticity equation, we obtain a three dimensional dissipative Boussinesq equation by the reduced perturbation method, i.e.utt+e1uxx+e2(u2)xx+e3utxy+e4uxxxx+e5uxxyy=0. It is emphasized that the new equation is different from the existing Boussinesq equations, which describe the three dimensional nonlinear Rossby waves in the atmosphere. Moreover, we explore the dispersion relation of the linear wave through the new equation. Using the travelling wave method and simplest equation method, the general solution and soliton solutions of the equation are obtained successfully respectively. Finally, the formation mechanism of Rossby waves is discussed by multiple soliton solutions.
Highlights
IntroductionIn the 20th century, Carl-Gustaf Rossby, a famous meteorologist, discovered a slow, large-scale wave in the Earth’s atmosphere, with a wave length of
In the 20th century, Carl-Gustaf Rossby, a famous meteorologist, discovered a slow, large-scale wave in the Earth’s atmosphere, with a wave length of Preprint submitted to Journal of LATEX Templates3000 km to 10000 km, and named Rossby waves
Many studies have shown that the evolution of Rossby waves is closely related to extreme weather phenomena, such as the Walker circulation,[1] atmospheric blocking,[2] the low-frequency Madden-Julian oscillation,[3] the ENSO.[4,5]
Summary
In the 20th century, Carl-Gustaf Rossby, a famous meteorologist, discovered a slow, large-scale wave in the Earth’s atmosphere, with a wave length of. A variety of three dimensional equations are obtained to characterize the formation of Rossby waves, in order to explain some weather phenomena more accurately in real atmosphere motions. For the exact solutions of high dimensional NPDEs, researchers have obtained many methods Such as generalized Homogeneous Balance Method,[26], Hirota’s bilinear method,[27−32] the tanh-coth method,[33] Backlund transformation,[34,35] trial function method,[36] auxiliary equation method,[37] the Fourier Galerkin and the KarhunenCLoeve (KCL) Galerkin numerical methods.[38] different NPDEs have different methods.
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