I'm having some trouble trying to decihper the notation used for the stream function in two dimensions.(adsbygoogle = window.adsbygoogle || []).push({});

Say we have a velocity field:

[tex] \vec V(x,y) [/tex]

The fluid is incompressible, thus Laplaces equation must be satisfied.

[tex] \nabla^2 u = 0 [/tex]

Where: [tex] u = \Nabla \vec V [/tex]

Thus: [tex] u_x = V_1 [/tex]

[tex] u_y = V_2 [/tex]

Where [itex] u_x [/tex] is short hand for the partial derivative of [itex] u(x,y) [/tex]

So now here comes the stream function.

Is it a vector function? It has to be right?

The definition I have is that the stream function satisfies:

[tex] u = -\nabla \times s(x,y)\hat k [/tex] (1)

Now the curl is supposed to return a vector right?

So how is this satisfied with (1). I'm guessing that it must deal with the [itex] \hat k [/tex]

But if someone could help me clear this up that would be cool. Also please, note that we are ONLY dealing with 2 dimensions for right now.

Thanks

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# Homework Help: Stream Function

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