I'm taking the curl of the deviatoric stress tensor in index notation, and I've ran across something that I can't seem to be able to simplify. The issue is shown in the following portion of the curl operation:
The first two terms on the right hand side should be zero because the curl of a scalar and the curl of a gradient of a scalar are zero. The last term will then be given by:
Since U has a subscript m on that last term on the RHS, then I can't just define it as the gradient of the vorticity like I did on the first term on the RHS. Is there any further way to simplify it or does that just have to be the curl of the gradient of velocity?