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I noticed that v [in step (2.5)] is not the same as the terms from the first formula, even if they are related..

I tried to understand how did he reach to this step:

enter image description here

I got a link (is found here) and still didn't understand the passing to (2.5). please help me to understand it.

any help appreciated!

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Related post by OP: physics.stackexchange.com/q/61289/2451 –  Qmechanic Apr 17 '13 at 23:39
    
I know but here I'm just asking for the step (2.5). –  Alon Shmiel Apr 17 '13 at 23:40
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Equation (2.5) expresses the velocity field in function of the stream function: en.wikipedia.org/wiki/Stream_function –  Christoph B. Apr 18 '13 at 8:19
    
@ChristophB. thank you Christoph! it helped me! –  Alon Shmiel Apr 18 '13 at 13:03

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