In order to incorporate the influence of turbulence in the Navier-Stokes equations the shear stress tensor is given by: $$\tau = \rho v_e(\nabla\mathbf{u}+\nabla(\mathbf{u})^T-2/3\nabla\cdot\mathbf{u}) \tag{3.4}$$
As I know, the result $\nabla\cdot\mathbf{u}$ is a scalar, meanwhile gradient of u is a tensor... can I expand the result of $\nabla\cdot\mathbf{u}$ to be size of tensor?