Do rigorous bounds restrict the growth of vortex knots?
ORAL
Abstract
In 2018 the growth of the enstrophy for trefoil vortex knots provided weak empirical evidence for the formation of a finite-time energy dissipation, known as a dissipation anomaly JFM 839, R2, 2018. This was achieved using an algebraic, not Gaussian, profile of the vorticity about the centerlines of the vortex knot and allowing the size of computational domain to increase as the viscosity decreased. These uncommon features can now be justified by new mathematics. First, instability analysis (Gallay/Smets Anal. PDE Vol. 13, 2020) shows that Gaussian profiles are unstable by applying the traditional formalism for boundary layers to the shear around vortex cores. The example algebraic profile is largely not unstable. The domain was increased due to mathematics that shows that for a fixed configuration, at very small critical viscosity the energy dissipation rate goes to zero, a restriction empirically broken by using larger domains. The new mathematics shows that extensions of the original proof do not prevent this, and might require it.
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Presenters
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Robert M Kerr
Univ of Warwick, University of Warwick
Authors
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Robert M Kerr
Univ of Warwick, University of Warwick