# OVD1-program

```eps = 0.1; gamma = 0.123; vnu = 3.2; tfinal = 3;

vor1[xnu_,ynu_,t] = 1/ynu - vnu+ eps xnu/gamma Sin[t/gamma];
vor2[xnu_, ynu_, t_] = -eps ynu /gamma Sin[t/gamma];
vortices =
NDSolve[{x1'[t]==vor1[x1[t], y1[t], t],
y1'[t] == vor2[x1[t], y1[t], t], x1[0] == 0, y1[0]==1}, {x1,
y1}, {t, 0, tfinal}];
xnu[t_]:= First[x1[t] /. vortices];
ynu[t_] := First[y1[t] /. vortices];
f[x_,y_,t_] := -((y-ynu[t])/((x-xnu[t])^2+(y-ynu[t])^2)-
(y+ynu[t])/((x-xnu[t])^2+(y+ynu[t])^2))- vnu+
eps x/gamma Sin[t/gamma];
g[x_, y_, t_ ]:= (x-xnu[t])*((y-ynu[t])/((x-xnu[t])^2+(y-ynu[t])^2)-
(y+ynu[t])/((x-xnu[t])^2+(y+ynu[t])^2))-
eps y/gamma Sin[t/gamma];
NumOfPoints=100;     (*Number of points on the boundary of parcels*)
(* Initial Centers of individual parcels*)
centers={{0.3, 0.3},{0.9, 0.9},{1.8, 1.8}};
interval = 0.03;       (*Time between snapshots*)
diffeqn[tfin_,aa_,bb_]:=NDSolve[{x'[t]==f[x[t],y[t],t],
y'[t]==g[x[t],y[t],t],
x[0]==aa, y[0]==bb},
{x,y}, {t,0,tfin}, MaxSteps->10000];
{w, 0, 2*Pi, 2*Pi/NumOfPoints}]];
oldsolution[i]=Table[diffeqn[tfinal,initdata[i][[j,1]],
initdata[i][[j,2]]], {j, Length[initdata[i]]}];
data[i]=Table[{x[t], y[t]} /. oldsolution[i], {t, 0, tfinal, interval}];
ColoredSnapshots[i]=Table[Graphics[{PointSize[0.01],
{RGBColor[1-0.2*i, 0.2*i, 0],
Map[Point, Flatten[data[i][[j]],1]]}}],  {j, Length[data[i]]}],
{i,Length[centers]}];

Do[
giffile=Show[Table[ColoredSnapshots[k][[i]],
{k,Length[centers]}],
PlotRange->{{-5,5}, {-3,3}},
AspectRatio->Automatic];
llabel=StringJoin[ToString[i],".gif"];
Display[llabel,giffile,"GIF"],
{i, Length[ColoredSnapshots[1]]}];
```