How Helicity Helps Create Finite Dissipation Without Singularities

Explore a 70-minute seminar lecture examining how helicity influences finite dissipation without singularities in fluid dynamics. Delve into Professor Robert Kerr's analysis of Navier-Stokes evolution involving interacting vortices, focusing on configurations where locally orthogonal vortices dominated by one sign of helicity shed oppositely signed vortex sheets. Learn about the critical role of viscosity's fourth-root in controlling temporal evolution of vorticity moments and computational domain growth. Understand the convergence patterns of volume-integrated enstrophy and their relationship to dissipation rates across various scenarios including trefoil vortex knots, interacting coiled vortex rings, and Taylor-Green vortex evolution. Discover how negative helicity vortex sheets spawn in pairs, leading to specific scaling patterns, and examine the implications for finite energy dissipation as viscosity approaches zero. The lecture, presented at the Isaac Newton Institute as part of the Anti-diffusive dynamics program, provides detailed mathematical analysis supported by research findings from multiple published studies.