Use Euler's equation to show that in a planar flow of an inviscid fluid the vorticity satisfies
Write down the velocity field associated with a point vortex of strength in unbounded fluid.
Consider now the flow generated in unbounded fluid by two point vortices of strengths and at and , respectively. Show that in the subsequent motion the quantity
remains constant. Show also that the separation of the vortices, , remains constant.
Suppose finally that and that the vortices are placed at time at positions and . What are the positions of the vortices at time ?