Points

The source filaments can be subjected to one more lumping step by dividing the £ coordinate into some number of intervals from £1 to £2, and lumping Л(£) over each interval into a point-source strength £. The filament integrals then become a sum of relatively simple algebraic expressions over the point sources.

The resulting velocity field is now even more singular than for the filaments, varying as |Vh| 1/Ar2

where Ar = | r — r’ | is the distance to the point.

Vortex filaments could be lumped into point point vortices or “vortons” in the same manner as the source filaments. However, in addition to having the |V| ~ 1/Ar2 singularity, the resulting velocity field is not exactly irrotational in the vicinity of each vorton. Hence, if perfect irrotationality is required away from the singularities, then equations (2.20) and (2.21) constitute the simplest possible velocity field representation via vortices and sources.