# Plot: 2D potential vortex embedded in 2D uniform flow

Consider a 2D potential vortex (having velocity $u_\theta = c/r$ in a quiescent environment) embedded in a 2D uniform flow (having a velocity of $u_x= U$ far away from the vortex) as below:

Question: For $U= 5m/s$, and $c = 0.5 m^2/s$, plot the velocity vectors for this flow on the domain {x,-0.3,0.3},{y,-0.3,0.3}

• Don't you need lots more information, such as the viscosity? – David G. Stork Feb 8 '17 at 20:11
• I don't think we need any other information in this particular problem. I think the matter is the interpretation of vortex flow with ambient flow, and the language of Mathematica plotting velocity vector field following the condition above. – Peter Feb 8 '17 at 20:16
• The basic strategy could be to use ImplicitRegion[] to define a region that that excludes the origin then use VectorPlot with that region. If you run into difficulties with this approach, add your code to your question so we can see exactly what the problem is. – LouisB Feb 8 '17 at 21:43

    StreamPlot[
{
{5, 0},
.5 {-y,x}/(x^2+y^2),
{5, 0} + .5 {-y,x}/(x^2+y^2)
},
{x, -.3, .3}, {y, -.3, .3},
StreamStyle -> {Red, Green, Blue},
PlotLegends -> {"Uniform", "Vortex", "Sum"}]


• The vortex component could be written more succinctly as 0.5 {-y, x}/(x^2 + y^2) – Simon Woods Feb 8 '17 at 22:20
• Yep... thanks. So edited. – David G. Stork Feb 8 '17 at 22:22
LineIntegralConvolutionPlot[
{5, 0} + .5 {-y,x}/(x^2+y^2)
,
{x, -.3, .3}, {y, -.3, .3}]