I thought about that, but that doesn't make sense. If we interpret the symbol as the outer product, then [itex](u,v)\otimes (u,v)[/itex] is a 2x2 matrix. But as I pointed out, it seems that

The quote in the original post tells you for certain that [itex]\textbf{u} \otimes \textbf{u}[/itex] is a tensor, as the tensor [itex]\tau_d[/itex] is being subtracted from it (and you can't substract a 2x2 tensor from a vector). Your deduction that [itex]\textbf{u} \otimes \textbf{u} = (\mathbf{u} \cdot \nabla) \mathbf{u}[/itex] is incorrect. How did you arrive at this conclusion?

it is clear that
[tex]
\textbf{u} \otimes \textbf{u}
[/tex]
has to be a tensor; I don't know where or why you have,
[tex]
\textbf{u} \otimes \textbf{u} = \textbf{u} \cdot \nabla \textbf{u}
[/tex]
but my guess is that it can't be correct.

What a confusing way to write the Navier-Stokes equations. I have no idea why the authors didn't just write them in the typical way everybody else uses without the tensor notation.