The curl of a (velocity) field can be defined as:
$\nabla\times\vec{u}=(\frac{\partial\,\omega}{\partial\,y}-\frac{\partial\,v}{\partial\,z})\vec{i}+(\frac{\partial\,u}{\partial\,z}-\frac{\partial\,\omega}{\partial\,x})\vec{j}+(\frac{\partial\,v}{\partial\,x}-\frac{\partial\,u}{\partial\,y})\vec{k}$
The question is: Does anyone know how such calculations work in practice? If I have a (f.e.) velocity field with 3 x 10 velocity values - can I calculate the curl at the same 3 x 10 points? Since partial derivatives have to be calculated, wouldn't I always use 2 adjacent vectors? If so, how exactly is this done?
I hope that my question is understandable. If not, please let me know.