__Kinematic Vorticity Number__

Flow lines represent the path followed by material particles or material lines during the progressive deformation. The kinematic vorticity number or Wk (Truesdel 1954, Ramberg 1975, Ghosh and Ramberg, 1976, Ghosh 1987 for Sr) vanishes or becomes zero for irrotational deformtion and is unity for rotational deformation exclusively by simple shear. For any deformation which is by combination of pure and simple shear the value of Wk is greater than zero but less than unity.

If Wk=0 then the particle paths or velocity field consists of a family of hyperbolae asymptotic to the two flow apophyses. If Wk=1, then the velocity field is purely defined by straight parallel lines. However, if the value of Wk is 1>Wk>0 then the deformation path is a combination of two, one for pure shear part and another for the simple shear component, i.e. of straight line segments and hyperbolae but asymptotic to the two acute ( -ve) and obtuse ( +ve) flow apophyses.

As shown by Ghosh and Ramberg, Sr or the rate of pure to simple shear will determine how fast the particle will rotate relative to the matrix given an axial ratio that is constant. Or the axial ratio large, the particle will have the rate of rotation as fast as the matrix markers.