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$\nabla({\bf u}^2)=2({\bf u}\cdot \nabla){\bf u} - 2(\nabla \times {\bf u}) \times {\bf u}$
Please see the next link: http://www3.kis.uni-freiburg.de/~peter/teach/hydro/hydro02.pdf
In (2.13), he used:
$$\nabla({\bf u}^2)=2({\bf u}\cdot \nabla){\bf u} - 2(\nabla \times {\bf u}) \times {\bf ...
