I don't know what vorticity is so I can not really understand your equation (e.g. in what space is your problem defined? what does pi mean? Does wi stand for weight?...).
I am wondering does it ever make sense to translate this into 2D?
- Does Vorticity make sense in 2D?
- In 3D, a cross product produces another vector while in 2D a cross product produces a scaler. However, if wi means some kind of weight in a direction, then in 2D you should be able to do something similar with tangent.