Exercise 1.

The ABC (Arnold-Beltrami-Childress) flow is defined as,

$$\left( \begin{array}{c}u \\ v \\ w \end{array} \right)= \lef... ... B \sin x + A \cos z \\ C\sin y + B \cos x \end{array} \right)$$ (1)

Show that the ABC flow is a static solution to the Euler equation and find the pressure field.

The Euler equation is the Navier-Stokes equation without viscosity,

$$\partial_t {\bf u} + {\bf u}\cdot \nabla {\bf u} = - \nabla p$$ (2)