Nonlinear Analysis of Tropical Waves and Cyclogenesis Excited by Pressure Disturbance in Atmosphere

The horizontal equations of motion for an inviscid homogeneous fluid under the influence of pressure disturbance and waves are applied to investigate the nonlinear process of solitary waves and cyclone genesis forced by a moving pressure disturbance in atmosphere. Based on the reductive perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies the Korteweg–de Vries equation with a forcing term (fKdV equation for short), which describes the physics of a shallow layer of fluid subject to external pressure forcing. Then, with the help of Hirota’s direct method, the analytic solutions of the fKdV equation are studied and some exact vortex solutions are given as examples, from which one can see that the solitary waves and vortex multi-pole structures can be excited by external pressure forcing in atmosphere, such as pressure perturbation and waves. It is worthy to point out that cyclone and waves can be excited by different type of moving atmospheric pressure forcing source.