Reconnection of wingtip vortices behind aircrafts is thought to be a cause of wake turbulence, detrimental to air traffic control. We observe the reconnection process for three initial vortex tube set-ups; anti-parallel, orthogonal and anti-parallel with axial flow. From these we are able to identify each of the different reconnection processes observed and discussed for the magnetic reconnection case but not necessarily the vortex reconnection case; of both 2D and 3D reconnection. We use a finite different method to solve the Navier-Stokes equation for a large array of points. We analyse the results of the first two scenarios for a range of Reynolds numbers to observe how the viscous term of Navier-Stokes affects the reconnection process. We were able to show that for an increase in $Re$ we would see an increase in the reconnection rate due to the formation of thinner and stronger vortex sheets which are necessary for a faster reconnection. For higher values of $Re$ we observed a Kelvin-Helmholtz instability within the vortex sheets and the formation of additional vortex rings during the reconnection process. We simulate a range of axial flow values to observe how kinetic helicity and twist evolve with reconnection. We were able to identify the loss of twist in the vortex tubes due to 3D reconnection known as 'slipping'. In these and the orthogonal runs we observed the generation of null pairs and the formation of a separator between them. We utilised the plots of both vorticity isosurfaces and vorticity fieldlines to observe and analyse the reconnection process where isosurfaces have been the norm for vortex reconnection observations in previous work. The vorticity fieldlines allow us to observe the orientation of vorticity during reconnection and allow us to observe both the 'threads' and 'bridges' and their evolution together.