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Uniform decomposition of velocity gradient tensor
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In this paper,the principal decomposition of the velocity gradient tensor[Vv]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.
Velocity gradientLiutexresistancefluid kinematics
Chenxi Ma、Chaoqun Liu
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Department of Mathematics,University of Texas at Arlington,Arlington,TX,USA
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