(* joukoshaw090311.m *)
Needs["Graphics`ComplexMap`"]
$DefaultFont={"Verdana",20};
$TextStyle={FontFamily->"Verdana",FontWeight->"Bold", FontSize->18};
PolarConformal[func_, radial_, polar_, options___] :=
Show[GraphicsArray[{PolarMap[# &, radial, polar,
            options,  DisplayFunction -> Identity],
	PolarMap[func, radial, polar, options, DisplayFunction -> Identity]
		}], DisplayFunction -> $DisplayFunction];
	
CartesianConformal[func_, xrange_, yrange_, options___] :=
Show[GraphicsArray[{
	CartesianMap[# &, xrange, yrange, options,  DisplayFunction -> Identity],
	CartesianMap[func, xrange, yrange, options, DisplayFunction -> Identity]
		}], DisplayFunction -> $DisplayFunction];


Joukowski[x_, y_, R_, vbl_, \[Theta]_] := 
Exp[I \[Theta]] *((vbl + x + I y) + (-x + Sqrt[R^2 - y^2])^2/(vbl + x + I y));

Do[PolarConformal[Joukowski[x, 0, 2, #, 0] &,  {2, 5}, {0, 2 Pi}, Lines -> 10,
     PlotPoints -> 40,
  PlotRange -> {{-6, 6}, {-6, 6}}], {x, 0.5, 0.0, -0.05}];

Do[PolarConformal[Joukowski[0.5, y, 2, #, 0] &,  {2, 5}, {0, 2 Pi}, 
    Lines -> 10, PlotPoints -> 40,
PlotRange -> {{-6, 6}, {-6, 6}}], {y, 1, -1, -0.1}]


Do[PolarConformal[Joukowski[0.5, 0.5, 2, #, \[Theta]] &,  {2, 5}, {0, 2 Pi}, 
    Lines -> 10, PlotPoints -> 40,
PlotRange -> {{-6, 6}, {-6, 6}}], {\[Theta], 0, Pi/4, Pi/16}]
