摘要
In this paper,the principal decomposition of the velocity gradient tensor[∇v]is discussed in 3 cases based on the discriminant∆:∆<0 with 1 real eigen value and a pair of conjugate complex eigen values,∆>0 with 3 distinct real eigen values,and∆=0 with 1 or 2 distinct real eigen values.The velocity gradient tensor can also be classified as rotation point,which can be decomposed into three parts,i.e.,rotation[R],shear[S]and stretching/compression[SC],and non-rotation point,we defined a new resistance term[L],and the tensor can be decomposed into three parts,i.e.,resistance[L],shear[S]and stretching/compression[SC].Example matric are also displayed to demonstrate the new decomposition.Connections of principal decomposition between 3 different cases,and between Resistance and Liutex will also be discussed.
