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i'm trying to draw an irrotational vortex with this function:

ListVectorPlot[Table[{-y/(x^2 + y^2), x/(x^2 + y^2)}, {x, -3, 3, 3}, {y, -3, 3, 3}]]

But as you can see this function has a singularity in the origin, so how can i exclude a certain range of values close to the origin?

Thanks?

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  • $\begingroup$ Could use If[] in Table[] to eliminate the singular points at the outset. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Oct 15, 2018 at 9:09
  • $\begingroup$ Thanks but how? If[x==y==0, ?, ?] $\endgroup$
    – MementoMori
    Commented Oct 15, 2018 at 9:16
  • 1
    $\begingroup$ Yes, like that. Table[If[x == y == 0, {0, 0}, (* stuff *)], (* stuff *)]. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Oct 15, 2018 at 9:23

3 Answers 3

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A bit hacky, but you can do this:

Quiet[
 ListVectorPlot[
  Table[
   {-y/(x^2 + y^2), x/(x^2 + y^2)}, 
   {x, -3, 3, 1}, {y, -3, 3, 1}
   ] /. Indeterminate -> 0
  ]
 ]

enter image description here

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$\begingroup$ 
ListVectorPlot[
Table[{y/(x^2+y^2+2),-x/(x^2+y^2+2)},{x,-3,3,0.3},{y,-3,3,0.3}],PlotTheme -> "Minimal"]

enter image description here

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You can pre-specify the points you wish to plot. Here's one way of doing so using CirclePoints, which allows you to easily specify a minimum radius:

With[{pts =
   Flatten[Table[CirclePoints[n/2, 4*n + 1], {n, 1, 6}], 1]},
 ListVectorPlot[
  N@Map[Replace[p : {x_, y_} :> {p, {-y, x}/(x^2 + y^2)}], pts]]]

vector plot

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