That's the thing!
When i do plug the U(theta) and U(r) into the Tau matrix in RTheta coordinate system i'll get nonzero elements for Tau(1,2) which is d(Utheta)/d(R). Subsequently, i decomposed it to R(ij) and S(ij). Consequently, i got R(1,2), R(2,1) and S(1,2) and S(2,1). The other elements are zero. All in all i got to the point that solid body vortex does rotates rotationally as well as it deforms!
