Vorticity and Flux of Vector Field ##\vec{f}## Explained

[Jhenrique]

The quantity $\vec{\omega} = \vec{\nabla} \times \vec{f}$ is called vorticity and is the measure of the local circulation of the vector field $\vec{f}$.

So, given the same vector field $\vec{f}$, is possible measure the local flux by $\vec{\nabla} \cdot \vec{f}$. This quantity has some special name?

 

[Matterwave]

You mean other than "divergence"?

 

[Jhenrique]

You mean other than "divergence"?

I'm thinking so-so like way:
The curl operation results the vorticity, so the divergence operation results the ... ?

 

[Matterwave]

The divergence results in the...divergence...why would you need another word for it, when you have a perfectly good word already?

The "vorticity" you mention as a name is only valid for the curl of the velocity field of a fluid. A general curl is called a curl...

For a fluid, the divergence of the velocity would be sinks or sources I suppose. Sinks being negative divergence and sources being positive divergence.

 

[Jhenrique]

"Vorticity" isn't just a name, is a quantity! Source and sink are just qualitative considerations, I'd want a physical quantity for the divergence of the velocity of a fluid.

 

[WannabeNewton]

http://en.wikipedia.org/wiki/Incompressible_flow

 

[Jhenrique]

Incompressible is analogous of irrotational...

 

[Matterwave]

Tell you what, why don't you come up with a name for it, and tell us how useful this classification is, and maybe we'll all use it.

In the standard literature the terms WBN and I gave you are basically it.

 

[Jhenrique]

Tell you what, why don't you come up with a name for it, and tell us how useful this classification is, and maybe we'll all use it.

In the standard literature the terms WBN and I gave you are basically it.

Really! Mathematical quantities that haven't physical application isn't useful. But, how I like very much of math, always exist a theoretical interetering for anything.