# Von Kármán Vortices

How may we vary vectors in

StreamPlot[{y, -Sin[x/2]}, {x, -4, 12}, {y, -4, 4},
StreamColorFunction -> "Rainbow", AspectRatio -> Automatic]


to obtain a Von Kármán Vortex Street type vectored stream flow (alternating rotation sense in succeeding vortices)?

• This doesn't seem like a Mathematica question ... it's more like a physics question. Note: it's Kármán, not Kàrmàn. – Szabolcs Jun 27 '15 at 11:11
• At least there is a tag here, elsewhere it may not go through. – Narasimham Jun 27 '15 at 11:34
• @Kattern : Thanks, I like to see vector changes pictured on either side of, for example a fluttering flag. Please feel free to suggest how I should change my question with this aim in view. – Narasimham Jun 27 '15 at 12:03
• Replace StreamColorFunction "Rainbow" by StreamColorFunction -> "Rainbow". – bbgodfrey Jun 27 '15 at 13:07
• @Kattern Is it possible to use Manipulate frames &c. to trace a few points embedded on the streamline? It c/should give an impression of dry leaves floating in the stream in video (around obstacles at center but free stream along x) caught by a stationary camera on riverbank. – Narasimham Jun 28 '15 at 5:36

Did you have something in mind like

StreamPlot[{(y - 2 Cos[x/4])  Cos[x/4], -Sin[x/4]}, {x, -4, 12},
{y, -6, 6}, StreamColorFunction -> "Rainbow", AspectRatio -> Automatic]


Another plot, this one with net flow.

dy = 3; flow = 1; sv = 6;
StreamPlot[{(y - dy Cos[x/4]) Exp[-(y - dy Cos[x/4])^2/sv]  Cos[x/4] +
flow (1 - Exp[-(y - dy Cos[x/4])^2/sv]),
-Sin[x/4] Exp[-(y - dy Cos[x/sv])^2/6]}, {x, -4, 18}, {y, -7, 7},
StreamColorFunction -> "Rainbow", AspectRatio -> Automatic]


The graphics choice suggested by chris makes the plot look even better.

dy = 3; flow = 1; sv = 6;
LineIntegralConvolutionPlot[{{(y - dy Cos[x/4]) Exp[-(y - dy Cos[x/4])^2/sv]
Cos[x/4] + flow (1 - Exp[-(y - dy Cos[x/4])^2/sv]),
-Sin[x/4] Exp[-(y - dy Cos[x/sv])^2/6]}, {"noise", 500, 500}}, {x, -4, 18},
{y, -6, 6}, AspectRatio -> Automatic, LineIntegralConvolutionScale -> 3]


• Yes right, vorticity of alternating whirlpools are same sign, also here in youtube towards the last part. The streamlines should be in x-direction always. youtube.com/watch?v=Gq-sUhP3kDI – Narasimham Jun 27 '15 at 18:36
• Gotta love the LineIntegralConvolutionPlots -- they're both cool and ugly at the same time. – Michael E2 Jun 27 '15 at 23:18
• Coool.. more than what I had expected.. Instead of brown another color combination could perhaps brighten it. – Narasimham Jun 28 '15 at 5:25
• Add as an option the colors of your choice, such as ColorFunction -> "Rainbow". By the way, please accept this answer, if it meets your needs. – bbgodfrey Jun 28 '15 at 5:44
• @chris Who can say? But, thanks. – bbgodfrey Jun 29 '15 at 2:21

Or, almost directly from the documentation

LineIntegralConvolutionPlot[{{(y - 2 Cos[x/4]) Cos[x/4], -Sin[x/4]},
, {"noise", 500, 500}}, {x, -4, 12}, {y, -6, 6},
StreamColorFunction -> "BeachColors", AspectRatio -> Automatic,
LightingAngle -> 0, LineIntegralConvolutionScale -> 3, Frame -> False]


• "A Study in Cut Timber" :D – J. M. will be back soon Jun 30 '15 at 0:55
• Annular rings.. more the merrier? – Narasimham Jul 4 '15 at 5:30