viscous force: Cfx : wrong formulation ????
 

I read from CFX 10.0 Theory Book, that Cfx uses this formulation for the viscous forces:

--------------------------------------------------------- Viscous Forces = coeff_viscous * (u_i,j+u_j,i),j --------------------------------------------------------- where: u_i := is the i-th component of the velocity u= (u,v,w)

and u_i,j = is the j-spatio-derivative by the j-th space direction.

from the Text book, the correct formulation, valid for all fluid (incompressible and compressible both) is:

--------------------------------------------------------- Viscous Forces = coeff_viscous * (u_i,j+u_j,i),j-2/3*(u_k,k)*delta_Kronecker(i,j) ---------------------------------------------------------

Why ???????????????