This chapter wraps up all results and findings in each of the four results sections: isolated vortices, chaotic tangle, vortex collider and Hopf link configurations. In the case of the isolated vortices and the chaotic tangle configurations, the results show that an energy equilibration regime starts to form when the Kelvin waves that form after vortex reconnections start to interact with each other, transferring energy from large to small scales. It was also found that disallowing reconnections, after the initial reconnections happen, aids in bringing forward the energy equilibration because the small scales stay in the larger tangle, rather than being expelled in the form of small vortex rings. In the case of the vortex collider and Hopf link configurations (vortex bundles), the results show that vortex stretching enables a k−5/3 scale in the energy spectra when the stretching of the bundle cores is such that the individual quantized vortices have clumped together sufficiently. In the case of the Hopf link configuration, the anti-parallel portions of the vortex bundle cores excite a Crow instability on the tangles that ultimately evolve into secondary structures that stretch enough to concentrate vorticity at small scales; this results in a k−5/3 scale in the energy spectra. Lastly, this chapter briefly discusses possible future lines of work, which involve further improving the acceleration of the algorithms to compute more complex and larger systems.

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Conclusions

  • Adrián M. Parrado Almoguera

摘要

This chapter wraps up all results and findings in each of the four results sections: isolated vortices, chaotic tangle, vortex collider and Hopf link configurations. In the case of the isolated vortices and the chaotic tangle configurations, the results show that an energy equilibration regime starts to form when the Kelvin waves that form after vortex reconnections start to interact with each other, transferring energy from large to small scales. It was also found that disallowing reconnections, after the initial reconnections happen, aids in bringing forward the energy equilibration because the small scales stay in the larger tangle, rather than being expelled in the form of small vortex rings. In the case of the vortex collider and Hopf link configurations (vortex bundles), the results show that vortex stretching enables a k−5/3 scale in the energy spectra when the stretching of the bundle cores is such that the individual quantized vortices have clumped together sufficiently. In the case of the Hopf link configuration, the anti-parallel portions of the vortex bundle cores excite a Crow instability on the tangles that ultimately evolve into secondary structures that stretch enough to concentrate vorticity at small scales; this results in a k−5/3 scale in the energy spectra. Lastly, this chapter briefly discusses possible future lines of work, which involve further improving the acceleration of the algorithms to compute more complex and larger systems.