Principal coordinates and principal velocity gradient tensor decomposition  

作　　者：Yifei Yu Pushpa Shrestha Charles Nottage Chaoqun Liu 

机构地区：[1]Department of Mathematics,University of Texas at Arlington,Arlington 76019,USA

出　　处：《Journal of Hydrodynamics》2020年第3期441-453,共13页水动力学研究与进展B辑（英文版）

摘　　要：Helmholtz velocity decomposition and Cauchy-Stokes tensor decomposition have been widely accepted as the foundation of fluid kinematics for a long time.However,there are some problems with these decompositions which cannot be ignored.Firstly,Cauchy-Stokes decomposition itself is not Galilean invariant which means under different coordinates,the stretching(compression)and deformation are quite different.Another problem is that the anti-symmetric part of the velocity gradient tensor is not the proper quantity to represent fluid rotation.To show these two drawbacks,two counterexamples are given in this paper.Then“principal coordinate”and“principal decomposition”are introduced to solve the problems of Helmholtz decomposition.An easy way is given to find the Principal decomposition which has the property of Galilean invariance.

关 键 词：Velocity decomposition HELMHOLTZ Cauchy-Stokes Liutex principal coordinate 

分 类 号：O183[理学—数学]