Direct numerical and large-eddy simulation of trefoil knotted vortices

Abstract

Abstract

Helicity dynamics in reconnection events of topologically complex vortex flows

“…This again confirms the conclusion drawn in Appendix A of the paper by Zhao et al. (2021), but from the helicity point of view.

Figure 14.Box-size sensitivity check on the trefoil knot case with mm.

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“…The flattening of curvature at tipping points in viscous reconnection has been reported by multiple numerical studies (Yao & Hussain 2020; Zhao et al. 2021). The radii of curvature reach a minimum value and then increase as the two vortex tubes approach each other.…”

“…Sensitivity to box size In Appendix A of the paper by Zhao et al. (2021), a sensitivity study on the box-size analysis is conducted, based on the trefoil-knot simulation, via a rigid two-point correlation analysis. It has been shown that a box size of can sufficiently minimize the artefacts from the boundary conditions.…”

“…With AMR, an increase of box size does not significantly affect the computational cost, as it would if a standard Cartesian grid was employed. Whereas the sensitivity study on the box size in Appendix A of the paper by Zhao et al. (2021) is performed based on kinetic energy and enstrophy, we here provide a new test for the sensitivity of the box size on the helicity result. As shown in figure 14, we used three different box sizes, and , to simulate the trefoil-knot case with mm, with the medium size being reported in the manuscript.…”

“…This is only achievable by relying on adaptive mesh refinement (AMR) computational frameworks such as that developed by the current authors (Zhao & Scalo 2020; Zhao et al. 2021).…”