# $\nabla({\bf u}^2)=2({\bf u}\cdot \nabla){\bf u} - 2(\nabla \times {\bf u}) \times {\bf u}$

In (2.13), he used: $$\nabla({\bf u}^2)=2({\bf u}\cdot \nabla){\bf u} - 2(\nabla \times {\bf u}) \times {\bf u}.$$

Is this is a formula? can someone let me some details/link about this formula?

Any help appreciated!

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See e.g. Wikipedia. –  Qmechanic Mar 9 at 13:46
Look at pg 68 of Panasatasiou et al.This is a fluid mechanics book available for free. –  drN Mar 9 at 14:17
$$(\nabla \times \vec u )\times \vec u = \epsilon_{ijk}(\nabla \times u)_j u_k = \\ \epsilon_{ijk}\epsilon_{jlm}\partial_l (u_m) u_k = \epsilon_{jki}\epsilon_{jlm}\partial_l (u_m) u_k = \\ (\delta_{kl}\delta_{im} - \delta_{km}\delta_{il}) \partial_l (u_m) u_k = \\ \partial_k (u_i) u_k - \partial_i (u_k) u_k = (\vec u \cdot \vec \nabla) \vec u - \frac 1 2 \nabla(\vec u \cdot \vec u)$$