Abstract
The evolution of nonlinear gravity solitary waves in the atmosphere is related to the formation of severe weather. The nonlinear concentration of gravity solitary wave leads to energy accumulation, which further forms the disastrous weather phenomenon such as squall line. This paper theoretically proves that the formation of squall line in baroclinic nonstatic equilibrium atmosphere can be reduced to the fission process of algebraic gravity solitary waves described by the (2 + 1)-dimensional generalized Boussinesq-BO (B-BO) equation. Compared with previous models describing isolated waves, the Boussinesq-BO model can describe the propagation process of waves in two media, which is more suitable for actual atmospheric conditions. In order to explore more structural features of this solitary wave, the derived integer order model is transformed into the more practical time fractional-order model by using the variational method. By obtaining the exact solution and the conservation laws, the fission properties of algebraic gravity solitary waves are discussed. When the disturbance with limited width appears along the low-level jet stream, these solitary waves can be excited. When the disturbance intensity and width reach a certain value, solitary wave formation takes place, which is exactly the squall line or thunderstorm formation observed in the atmosphere.
Highlights
On June 4, 2016, a squall line weather occurred in northern Sichuan, China, lasting for 12 hours
E phenomenon of gravitational waves occurring in the upper atmosphere is the most common and important dynamic process. ey propagate in the middle atmosphere and generate energy and momentum transfer between atmospheres at different altitudes, which leads to the process of energy coupling between atmospheres [1]. e pressure jump, strong wind, strong convergence, and upward movement of gravity waves are caused by nonlinear action in the dispersion process
In 2000, Scinocca and Ford [17] found that large gravity solitary waves forced unstable layered shear flows. It can be seen from previous studies that the research on gravity waves and squall line mainly focuses on numerical simulation, while the research on theoretical analysis is very few
Summary
On June 4, 2016, a squall line weather occurred in northern Sichuan, China, lasting for 12 hours. En, in 2014, Srinivasan et al [15] studied the gravitational wave characteristics of squall line during its propagation. In 2000, Scinocca and Ford [17] found that large gravity solitary waves forced unstable layered shear flows It can be seen from previous studies that the research on gravity waves and squall line mainly focuses on numerical simulation, while the research on theoretical analysis is very few. Because of the baroclinic characteristics of the atmosphere, the baroclinic problem in the actual atmosphere is inevitable These studies describe classical gravity solitary waves [22, 23]. Erefore, we need to establish a new model to replace the classical gravity solitary waves and explore the formation mechanism of squall line so as to better adapt to the actual atmospheric conditions. Because fractional derivatives are historically dependent and nonlocal, they can more accurately describe complex physical and dynamic system processes in nature. e solution of fractional-order equation has attracted more and more attention of scholars, who have studied many effective solutions, such as the (G’/G)-expansion method [35], Khater method [36], sun-equation method [37], functional variable method [38], modified extended Tanh method [39], Godunov-type method [40], Lie group analysis method [41], and so on [42,43,44,45]
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