What does curl(U)=0 mean physically for a fluid element?

[Baggio]

All the math based texts just simply derive or state curl(U)=0 but what does this physically mean?

Does it mean that a single fluid element does not rotate?

 

[dextercioby]

It means that the velocity vector field is a conservative one,as it comes from a scalar potential (due to curl=0).Yes,the condition is called "irrotational flow" for good reason;basically the fluid lines do not curl,they are parallel wrt themselves at any moment of time.
http://discover.edventures.com/functions/termlib.php?action=&termid=532&alpha=r&searchString=

Daniel.

 

[Gokul43201]

I suspect a good intro to superfluidity will cover this nicely ... let me check if I've got something bookmarked.

 

[dextercioby]

I would suspect an equivalent term for it would be:"laminar flow".

But that's just terminology.The basic idea behind is relevant.

Daniel.

EDIT:It would be really dull,if i wasn't wrong from time to time,huh...?

 

[arildno]

There is no connection between the concepts "laminar flow" and "irrotational flow".
Couette flow is certainly laminar, but not at all irrotational.
Irrotational means what it says: the local angular velocity at a point is zero.

EDIT: Yes, I think I would yawn myself to death if you were right all the time..
(Possibly, that's what I ought to do, anyways?? )

 

[Baggio]

I thought so, thanks.