Three vortex motion in the slightly viscous flow

作     者：ZHU Hao & CHENG KeMing College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 

作者机构：College of Aerospace Engineering Nanjing University of Aeronautics and Astronautics Nanjing China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2010年第53卷第4期

页      面：735-744页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：point vortex slightly viscous flow Fokker-Planck equation collapse Ito formula 

摘      要：The dynamics of three vortices moving in an ideal fluid in a plane can be expressed in Hamiltonian form. However, when viscosity can not be ignored, the system of point vortices has not this delicious structure. This investigation focuses on the viscosity effect on the motion of three vortices. Since the viscous diffusion of vortices is simulated by Brownian motion, the equations of intervortical distances are obtained by Ito formula. These equations show that there exist two viscosity effects on intervortical distances: stable expansion and random impulse. Furthermore, via employing the asymptotic solution to these equations, these two viscous effects have been shown to destroy the self-similar process of collapse and make it into a new configuration, which is similar to the near collapse in the ideal case.