Another example

This function is interesting in that its divergence may not be what you think it is.

In[219]:=

  vF2[x_,y_] := {x Cos[y], -Sin[y]}

We can look at the vector field.

In[220]:=

  PlotVectorField[vF2[x,y],{x,-5,5},{y,-5,5},Axes->True];

Where are the sources and sinks? Looking at the plots above, it is rather hard to tell. There is obviously a lot of circulation in this field, but there aren't any obvious sources or sinks. Let's compute the divergence.

In[221]:=

  div2[vF2][x,y]

Out[221]=

  0

Answer:

Answer: ...

Up to Divergence