What Is the Equation for a 3-Dimensional Stream Function?

[stan]

hi

does anyone know the equation for a 3-dimensional stream function?

for a 2 dimensional case, u=d(stream function)/dy and
v=-d(stream function)/dx..


so does anyone knows how to express u, v and w in terms of the stream function for a 3-dimensional case...

thanks.



stan

 

[Clausius2]

hi

does anyone know the equation for a 3-dimensional stream function?

for a 2 dimensional case, u=d(stream function)/dy and
v=-d(stream function)/dx..


so does anyone knows how to express u, v and w in terms of the stream function for a 3-dimensional case...

thanks.
stan

I have never seen a tridimensional stream function, although it exists. In words of Anderson in his book of Computational Fluid Dynamics and Heat Transfer:

"For the case of 3-d flows, it is possible to use two stream functions to replace the continuity equation. However, the complexity of this approach usually makes it less atractive than using the continuity equation in its original form".

Try to derivate it using two stream functions.

 

[devrana01]

stream function for three dimensional flow also exists but only for axisymmetric flow i.e the flow properties in the third direction(say z axis) is same or in other words the derivative w.r.t (d/dx)that, will be zero.

 

[Topher925]

stream function for three dimensional flow also exists but only for axisymmetric flow i.e the flow properties in the third direction(say z axis) is same or in other words the derivative w.r.t (d/dx)that, will be zero.

I agree. Stream functions in general do not exist in three dimensions, but only in a special case. Of course 3D stream functions exist physically but can not be represented mathematically.