I have a velocity vector with components in the $x$, $y$ and $z$ directions. Each component is some function of $x$, $y$ and $z$. How would I evaluate the location, (cartesian coordinates) of the maximum speed (extrema)?
Here is an example where gamma, $\gamma$, is a constant:
$$\mathbf{u}_3=\frac{2}{\sqrt{4\gamma^2+\pi^2}}\begin{pmatrix}0\\2\gamma\cos\left(\frac{\pi y}{2}\right)\cos(\gamma z)\\\pi\sin\left(\frac{\pi y}{2}\right)\sin(\gamma z)\end{pmatrix}$$