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New mathematics, numerical analysis and graphics applied to the interaction of very long and relatively thick anti-parallel vortex tubes is applied to new simulations with either thinner initial tubes or hollowed out tubes in order to investigate how the existing results will change as the singular limits of infinite thin lines and thin sheets are approached. Preliminary results are largely consistent with the existing results just submitted to J. Fluid Mechanics [1], with some notable differences. This abstract will only present the submitted JFM results. The new mathematics is based on a new rescaling of the vorticity moments, providing a way to compare through incremental orders the two extremes, the maximum of vorticity and enstrophy. In all simulations tested to date [2], the order of the rescaled moments is opposite to how the raw moments by Hölder inequalities. Using this new tool, the new thick tube calculations have shown the existence of a strong attraction to behaviour consistent with a singularity in a finite time, while also showing an inconsistency in how the two limiting moments grow.
Author(s):
Robert Kerr
University of Warwick
United Kingdom