does every incompressible flow have stream function ?

Posted on 2013-09-13
Medium Priority
Last Modified: 2013-09-25
So i have a streamline function f (x,y) it automatically satisfies continuity and flow is incompressible.
But what about the reverse ?
Can we say that every incompressible flow has a streamline function ?

Any link for further studying would be appreciated.
Question by:c_hockland
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aburr earned 668 total points
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here are two links which have lots of information
The first will have additional references
the second is a pdf which you can download for later study

Incompressible flow - Wikipedia, the free encyclopedia
In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a ...
¿Derivation - ¿Relation to compressibility - ¿Relation to solenoidal field

Lectures in computational fluid dynamics of incompressible flow
by JM McDonough - ¿Related articles
LECTURES in. COMPUTATIONAL FLUID DYNAMICS of. INCOMPRESSIBLE FLOW: Mathematics, Algorithms and Implementations. J. M. McDonough.
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ozo earned 664 total points
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Author Comment

ID: 39492006
i went through already the wiki article but it doesnt lnclude a proof that every incompr. flow has streamline function.....
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GwynforWeb earned 668 total points
ID: 39492052
Q: "Can we say that every incompressible flow has a streamline function"

Technically the answer to this is NO. Physically, incompressible turbulent flows do not have a stream function. This is because they are not laminar. They will have a stream function only in the sense of when local averaging is used.

However if the velocities u and v are well defined and differentiable then yes, a stream function will exist. The stream function being obtained through solving Poisson's equation together with the boundary conditions.

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