# Compute 3D stream surfaces?

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 April 24, 2013, 10:33 Compute 3D stream surfaces? #1 Senior Member   Jonas T. Holdeman, Jr. Join Date: Mar 2009 Location: Knoxville, Tennessee Posts: 108 Rep Power: 10 It is stated that 3D flow can be represented by two scalar stream surfaces. From these, the velocity field can be computed, and stream lines are the intersection of the surfaces. For instance in "2D flow", one surface might be the stream function and the other a set of parallel planes, with intersections projected onto one of the planes showing the stream lines via contour plots. But for general 3D flow, how might one compute the two stream surfaces on a mesh, either from the flow, or from the governing equations? Last edited by Jonas Holdeman; April 24, 2013 at 10:35. Reason: spelling

April 24, 2013, 12:18
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Filippo Maria Denaro
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Quote:
 Originally Posted by Jonas Holdeman It is stated that 3D flow can be represented by two scalar stream surfaces. From these, the velocity field can be computed, and stream lines are the intersection of the surfaces. For instance in "2D flow", one surface might be the stream function and the other a set of parallel planes, with intersections projected onto one of the planes showing the stream lines via contour plots. But for general 3D flow, how might one compute the two stream surfaces on a mesh, either from the flow, or from the governing equations?
Hi,
this is an interesting question for me, just have some ideas to work on.
Starting by the definition you have a potential vector such that

v = curl Psi

that involves 3 scalar functions. Defining a sarface that has zero normal velocity component would lead to satisfy the constraint

n.curl Psi = 0

Now I am thinking to the analogy with a vortical tube, where the surface of the tube is constrained to have zero normal vorticity (see the book of Chorin and Marsden).
Could we construct the stream surface in the same way?

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