This chapter presents the findings of this work, which were obtained by computing the previously mentioned algorithms and numerical methods for the physical models that were previously described. There are four different results sections, one for each type of vortex configuration. The first section talks about the energy spectra of isolated quantized vortices, the spectral signature of the Kelvin wave regime and of the energy equilibration in the system. Here, vortex stretching is not considered due to the nature of the quantized vortex cores, but the calculations focus on understanding the energy equilibration of the system triggered by Kelvin waves interacting with each other. The second section involves a system of chaotic vortex filament rings arranged randomly within a periodic cube. In this section, the same physics are studied; energy equilibration through the transfer of energy from large to small scales. In this configuration, there are many more vortex reconnections which were found to “vaporize” the tangle and remove small scales from it; this is counter-productive for the energy equilibration. A calculation was made where reconnections were disallowed after some reconnections happened to study the effect of interacting Kelvin waves on the energy distribution. The last two sections focus on the physics of quantized vortex bundles and therefore study the effects of vortex stretching on the energy distribution of the system; this is done for a vortex collider and a Hopf link configuration. The vortex stretching was studied in three different ways; dynamic vortex stretching achieved through the interaction between quantized vortex bundles, kinematic stretching (the manual stretching of the vortex bundles while maintaining the original vortex bundle volume) and the vortex bundle core reduction at t = 0 s while maintaining a constant bundle radius.