A new ZK-ILW equation for algebraic gravity solitary waves in finite depth stratified atmosphere and the research of squall lines formation mechanism. (English) Zbl 1416.86008
Summary: The research of algebraic gravity solitary waves is an advanced field which has important practical and theoretical value in physical, oceanography, aerology and etc. By calculation condition and theoretical method limit, previous researches mainly focused on the \((1+1)\) dimensional models, and \((2+1)\) dimensional models were few considered. In this paper, from the non-static equilibrium equation, a new ZK-ILW equation is derived by using multi-scale analysis and perturbation method in finite depth stratified atmosphere, which is the first time obtained. The model can reduce to ZK-BO model \((h\rightarrow\infty)\), and ZK model \((h\rightarrow 0)\) and is the generalization of the above two models. In order to further understand the nature of algebraic gravity solitary waves, we get the analytical solution of ZK-ILW equation by using the trial function method and discuss the conservation laws. Furthermore, the fission process of algebraic gravity solitary waves is studied, and we can judge that one of the possible formation mechanism of squall lines is the fission of algebraic gravity solitary waves.
MSC:
| 86A10 | Meteorology and atmospheric physics |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
Keywords:
\((2+1)\) dimensional algebraic gravity solitary waves; ZK-ILW equation; finite depth stratified atmosphere; trial function method; squall linesReferences:
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