Another example
vF2[x_,y_] := {x Cos[y], -Sin[y]}We can look at the vector field.
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.
div2[vF2][x,y]
Answer:
Up to Divergence