Exercise 2.

Show the vector identity:

$$\overline{\nabla}\times(\overline{u}\cdot\overline{\nabla})\overline{u} =$$ (1)

$$(\overline{u}\cdot\overline{\nabla})(\overline{\nabla}\times\over... ...e{u} +(\overline{\nabla}\cdot\overline{u})(\overline{\nabla}\times\overline{u})$$

This is used in deriving the vorticity equation. Use formulas from mathematical handbooks or do it by inspection, the last way is rather tideous ...