Program Physics and mathematics of turbulence in different media – 2026-09-16
Name: Renzo Ricca
Event: Program Physics and mathematics of turbulence in different media
Event URL: view webpage
Title: A Topological Approach to Turbulence Cascade
Date: 2026-09-16 @11:00 AM
Location: SCGP 102
Download the slides: 20260916_Ricca.pdf
Abstract: Superfluid turbulence is a phenomenon characterized by the production of large-scale structures made by complex tangles of vortex filaments that gradually decay to form small-scale loops. A topological analysis of superfluid tangles shows [1-3] that very complex knots and links upon continual interaction and reconnection tend to untie to form small, unknotted, unlinked vortex rings. Here we present a topological approach to turbulence cascade based on the idea that the dynamical process can be viewed in terms of geodesic flows in an appropriate knot polynomial space. This is done by using appropriately adapted polynomials of knot theory [4] to quantify the generic topological cascade of vortex knots observed in experiments. Optimal evolutionary unlinking paths can thus be determined and put in relation with observational data and energy cascade [5]. Further work in this direction is in progress [6].
This is joint work with Xin Liu (Beijing U. Technology, China).
[1] Cooper, R.G., Mesgarnezhad, M., Baggaley, A.W. & Barenghi, C.F. 2019 Knot spectrum of turbulence. Sci. Rep. 9, 10545.
[2] Barenghi, C.F. 2024 Tangled vortex lines: dynamics, geometry and topology of quantum turbulence. In Knotted Fields (ed. R.L. Ricca & X. Liu), pp. 243-279. Lecture Notes in Mathematics 2344, Springer-Nature, Switzerland.
[3] Guan, H., Zuccher, S. & Liu, X. 2025 Topological cascade of quantum Borromean rings. Phys. Fluids 37, 024126.
[4] Ricca, R.L. & Liu, X. 2026 A new framework for the Jones polynomial of fluid knots. JKTR 35, 2340024.
[5] Liu, X., Ricca, R.L., Li, X.-F. 2020 Minimal unlinking pathways as geodesics in knot polynomial space. Comm. Physics 3, 136.
[6] Liu, X., Ricca, R.L. & Zhuo, Y. 2026 Quantifying the hierarchical topological decay of fluid knots. Submitted.