AI 中文总结
本研究提出含内部垂直风切变的龙卷风状涡旋轴对称模型，获其精确粘性Feynman-Kac表示，揭示垂直切变下涡旋变形规律及长时间极限特征，或可解释龙卷风着陆后迅速减弱的现象。
AI 中文摘要
本注记提出了一个包含内部垂直风切变的龙卷风状涡旋的轴对称模型。通过采用规定的不可压缩环流-应变流来捕捉垂直风的水平变化，我们表明该模型对龙卷风结构具有精确的粘性Feynman-Kac表示。在存在涡旋垂直切变的情况下，倾斜项会诱导径向相位混合，从而快速变形涡旋结构，导致最大方位风的半径扩大并向上移动。在长时间极限下，涡旋趋近于Burgers径向尺度，同时风与涡度均呈指数衰减。这类解或可解释为何龙卷风在着陆后出现内部垂直切变结构后往往迅速减弱。
英文摘要
This note presents an axisymmetric model of a tornado-like vortex with internal vertical wind shear. By employing a prescribed incompressible circulation-strain flow that captures the horizontal variation of the vertical wind, we show that the model admits an exact viscous Feynman-Kac representation for the tornado structure. In the presence of vortex vertical shear, the tilting term induces radial phase mixing that rapidly deforms the vortex structure, thus causing the radius of the maximum azimuthal wind to broaden and shift upward. At the long-time limit, the vortex approaches the Burgers radial scale while both the wind and vorticity decay exponentially. This class of solutions may help explain why tornadoes often weaken rapidly once an internal vertical shear structure emerges after touchdown.
