Fractional Theoretical Model for Gravity Waves and Squall Line in Complex Atmospheric Motion

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.