Analytical Solution Of The Dynamic Pattern When Typhoon Intensity Changes The Fastest

China is one of the countries most seriously affected by typhoons in the world.The landing sites of typhoons are almost all over the coastal areas from South China to Northeast China.Therefore,the accurate prediction of typhoon is particularly important.Since the 1990 s,although China has made remarkable progress in typhoon path prediction,the progress in the prediction of typhoon structure and intensity change is slow,which can not meet the increasing needs of typhoon prevention and disaster reduction.Against this background,research on the typhoon intensity change and the influence of the asymmetric structure on the typhoon intensity is a major issue related to the national economy and people's livelihood,and it is the focus of the scientific research.Therefore,this paper studies the analytical solution of dynamic pattern when typhoon intensity changes the fastest,in order to provide a new theoretical direction for studying the motion mechanism and hierarchical structure of the typhoon.The main work of this paper is summarized as follows:Firstly,the energy functional is defined according to the kinetic energy equation in the rotating coordinate system,and the variational method is used to optimize the energy equation from the dynamic composition with the largest change rate of typhoon intensity.It is concluded that when the change rate of typhoon intensity reaches the maximum,the friction,the pressure gradient force,the gravity and the gradient of kinetic energy are balanced.The rapid intensification of typhoon Rammasun(2014)is simulated by the mesoscale model WRF,and the conclusion of the four-force balance is used to determine that the intensity change rate of typhoon Rammasun reaches the maximum at 12:00 on July 17,which proves the rationality of the conclusion.Secondly,the method of variational decomposition is used to extract the rotational flow in the wind field when typhoon intensity changes the fastest.The Euler-Lagrange equations satisfying the rotational and irrotational flow field are obtained,and the expression of the wind profile is obtained.The overall structure of typhoon depends on the wind profile H(z),and ? is the main parameter that determines H(z),so ? determines the hierarchical structure of typhoon.The wind field is then decomposed directly,and the obtained vorticity equation is consistent with the result of variational decomposition,which shows the feasibility of using variational method to decompose typhoon wind field.Finally,the constant variation method is used to solve the vorticity equation in polar coordinates,and the analytical solutions of the vorticity and the rotational field are obtained.It is further obtained through numerical experiments that when 0? =,the plot of streamline and stream function basically show a uniform gradient distribution,which is consistent with the measured flow field.When 0?(29),the plot of streamline and stream function of n =0 conform to the measured flow field distribution.The analytical solution of the dynamic pattern when typhoon intensity changes the fastest is obtained finally.It provides certain theoretical guidance for typhoon track and intensity forecast,and has certain practical value for studying the variation trend of velocity and the structure of flow field in the evolution of typhoon.