A new framework for the Jones polynomial of fluid knots

Here we illustrate how Jones’ polynomials are derived from the kinetic helicity of vortical flows, and how they can be used to measure the topological complexity of fluid knots by numerical values. Relying on this new findings, we show how to use our adapted Jones polynomial in a new framework by introducing a knot polynomial space whose discrete points are the adapted Jones polynomials of fluid knots, interpreting the topological simplification associated with the natural decay of reconnecting fluid knots as geodesic flows on this space.