Q  9.6  fz=U(z+a^2/z)+I Γ/(2 Pi)Log[z]   p.233

para = {U ->  1, a -> 1}

fz = 
      U (z + a^2/z) + I Γ/(2 Pi) Log[z]

V = Conjugate[D[fz, z] /. z -> z[t]]

step1  Γ=0      問9.4図(a)

eq = z'[t] == V /. Γ ->  0 /. 
        para

ne = 40;
z0 = Table[-20 - 2  I + 0.25 I i, {i, 0, ne}];

zuall = 
      Table[{ans = NDSolve[{eq, z[0] == z0[[i]]}, 
                z[t], {t, 0, 40}][[1]]; 
          ParametricPlot[Evaluate[{Re[z[t]], Im[z[t]]} /. ans], {t, 0, 40}, 
            PlotStyle ->  Hue[0.7], 
            PlotRange ->  {{-5, 5}, {-2, 2}}, 
            DisplayFunction ->  Identity]}, {i, ne}]

zu1 = 
      Show[zuall, Graphics[Disk[{0, 0}, 1]], 
        DisplayFunction ->  $DisplayFunction, 
        AspectRatio ->  Automatic]

step2.1 Γ=4 Pi a U    問9.4図(b)

eq = z'[t] == 
            V /. {Γ -> 
              0.5 4 Pi a U}/.para

ne = 25;
z0 = Table[-20 - 5.5  I + 0.25 I i, {i, 0, ne}];

zuall = 
      Table[{ans = NDSolve[{eq, z[0] == z0[[i]]}, 
                z[t], {t, 0, 40}][[1]]; 
          ParametricPlot[Evaluate[{Re[z[t]], Im[z[t]]} /. ans], {t, 0, 40}, 
            PlotStyle ->  Hue[0.7], 
            PlotRange ->  {{-5, 5}, {-3, 2}}, 
            DisplayFunction ->  Identity]}, {i, ne}]

zu21 = 
      Show[zuall, Graphics[Disk[{0, 0}, 1]], 
        DisplayFunction ->  $DisplayFunction, 
        AspectRatio ->  Automatic]

step2.2 Γ= 1 * 4 Pi a U     問9.4図(c)

eq = z'[t] == 
            V /. {Γ -> 
              1 4 Pi a U}/.para

ne = 40;
z0 = Table[-20 - 8  I + 0.25 I i, {i, 0, ne}];

zuall = 
      Table[{ans = NDSolve[{eq, z[0] == z0[[i]]}, 
                z[t], {t, 0, 40}][[1]]; 
          ParametricPlot[Evaluate[{Re[z[t]], Im[z[t]]} /. ans], {t, 0, 40}, 
            PlotStyle ->  Hue[0.7], 
            PlotRange ->  {{-5, 5}, {-3, 2}}, 
            DisplayFunction ->  Identity]}, {i, ne}]

zu22 = 
      Show[zuall, Graphics[Disk[{0, 0}, 1]], 
        DisplayFunction ->  $DisplayFunction, 
        AspectRatio ->  Automatic]

step2.3 Γ= 1.4 * 4 Pi a U    問9.4図(d)

eq = z'[t] == 
            V /. {Γ -> 
              1.4 4 Pi a U}/.para

ne = 40;
z0 = Table[-20 - 8.5 I + 0.4 I i, {i, 0, ne}];

zuall = 
      Table[{ans = NDSolve[{eq, z[0] == z0[[i]]}, 
                z[t], {t, 0, 50}][[1]]; 
          ParametricPlot[Evaluate[{Re[z[t]], Im[z[t]]} /. ans], {t, 0, 50}, 
            PlotStyle ->  Hue[0.7], 
            PlotRange ->  {{-5, 5}, {-3, 2}}, 
            DisplayFunction ->  Identity]}, {i, ne}]

zu23 = 
      Show[zuall, Graphics[Disk[{0, 0}, 1]], 
        DisplayFunction ->  $DisplayFunction, 
        AspectRatio ->  Automatic]

step3 Γ=4 Pi a U and Joukowski    問9.4図 (e) and (f)

w = z + 1/z /. z -> -0.5 +  I 0.5 + 1.58 z

zu30 = 
      ParametricPlot[{Re[w /. z ->  Exp[I θ]], 
          Im[w /. z ->  Exp[I θ]]}, {θ, 0, 2 Pi}, 
        PlotStyle ->  Hue[0.9], 
        PlotRange -> {{-5, 5}, {-4, 4}}]

eq = z'[t] == 
            V /. {Γ ->  
              0.5 4 Pi a U}/.{U ->  1, 
          a -> 1}

ne = 50;
z0 = Table[-20 - 7.5 I + 0.25 I i, {i, 0, ne}];

zuall = 
      Table[{ans = NDSolve[{eq, z[0] == z0[[i]]}, 
                z[t], {t, 0, 50}][[1]]; 
          ParametricPlot[
            Evaluate[{Re[w], Im[w]} /. 
                  z ->  Exp[I 0  °] z[t] /. ans], {t, 0, 
              50}, PlotStyle ->  Hue[0.7], 
            PlotRange ->  {{-8, 8}, {-5, 5}}, 
            DisplayFunction ->  Identity]}, {i, ne}]

zu31 = 
      Show[zuall, zu30, DisplayFunction ->  $DisplayFunction, 
        AspectRatio -> 0.3]

zuall = 
      Table[{ans = NDSolve[{eq, z[0] == z0[[i]]}, 
                z[t], {t, 0, 50}][[1]]; 
          ParametricPlot[
            Evaluate[{Re[w], Im[w]} /. 
                  z ->  Exp[I 30  °] z[t] /. ans], {t, 0, 
              50}, PlotStyle ->  Hue[0.7], 
            PlotRange ->  {{-8, 8}, {-5, 5}}, 
            DisplayFunction ->  Identity]}, {i, ne}]

zu32 = 
      Show[zuall, zu30, DisplayFunction ->  $DisplayFunction, 
        AspectRatio -> 0.3]

summary

Show[
      GraphicsArray[{{zu1, zu21}, {zu22, zu23}, {zu31, zu32}}]]