does every incompressible flow have stream function ?

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.
c_hocklandAsked:
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aburrCommented:
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
 en.wikipedia.org/wiki/Incompressible_flow¿
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




PDF]
Lectures in computational fluid dynamics of incompressible flow
 www.engr.uky.edu/~acfd/me691-lctr-nts.pdf¿
by JM McDonough - ¿Related articles
LECTURES in. COMPUTATIONAL FLUID DYNAMICS of. INCOMPRESSIBLE FLOW: Mathematics, Algorithms and Implementations. J. M. McDonough.
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ozoCommented:
yes
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c_hocklandAuthor Commented:
i went through already the wiki article but it doesnt lnclude a proof that every incompr. flow has streamline function.....
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GwynforWebCommented:
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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