Here the Paraview pipeline for generating the uniformly distributed vectors.
Load your foam file.
Goto Sources > Plane
and generate a plane of the desired dimensions and locations. 2m x 2m at the (0 0 0) point in this case.
Use "X Resolution" and "Y Resolution" to control the number of vectors to be plotted later. Using the same number here makes sense.
Now we map the results onto this plane.
Filters > Resample with Dataset
In the dialog pop up, select "Input" and click on your foam data.
Then select "Source" and click on the Plane.
Then click "Ok".
This will result in this:
You can now for example apply the calculator as Koldskaal mentioned to get rid of the U_x component in the U vector. Note formula, how "iHat" is multiplied with "0". This is purely done to make the vectors more "visible" in a y-z section, otherwise their length would be entirely ruled by the dominating x-component.
Create your "Glyph" filter on the Calculator, using the "Result" vector as an input and choose "All Points" for masking.
Play around with the X and Y Resolution on the Plane to quickly get a good looking plot.