台风强度变化最快时涡度的解析解

利用旋转坐标系中的基本方程推导得到动能方程，通过动能的局地变化率定义刻画台风强度变化率的能量泛函，对泛函作变分得到Euler-Lagrange方程.分析方程可知，当台风强度变化率达到最大时，摩擦力、气压梯度力、重力和动能梯度满足四力平衡关系.因此，这四个力确定的向量可以作为台风强度的预报因子，更准确地确定台风系统强度变化率达到最大的时间点.进一步通过风场变分分解提取到有旋场中的最大涡旋，得到台风强度变化最快时涡度和流场的解析解，对研究台风发展过程中速度的变化趋势和台风的空间结构具有实用价值，为台风路径和强度预报提供了一定的理论指引.

Analytical solution of vorticity when tropical cyclone intensity changes the fastest

In this study,the kinetic energy equation is derived from the basic equation in the rotating coordinate system,and then the energy functional describing the change rate of Tropical Cyclone (TC) intensity is defined by the local change rate of kinetic energy.Afterwards,the Euler-Lagrange equation is obtained by taking the variation of the functional.The equation shows that when the change rate of TC intensity reaches the maximum,the friction,the pressure gradient force,the gravity and the gradient of kinetic energy are balanced.Therefore,the vector determined by these four forces in the balance equation can be used as a predictor of TC intensity,which can more accurately determine the time when the intensity change rate of TCs reaches the maximum.Furthermore,the maximum vortex in a rotational field is extracted by the variational decomposition of wind field,and the analytical solution of vorticity and flow field are obtained when TC intensity changes the fastest.The conclusion has certain practical value for studying the variation trend of velocity and the spatial structure of TC in the evolution of TC,and provides certain theoretical guidance for TC track and intensity forecast.