Alexander Migdal (New York University Abu Dhabi) | Quantum Geometry of Classical Turbulence |


We argue that in the strong turbulence phase, as opposed to the weak one, the Clebsch variables compactify to the sphere S2 and are not observable as wave excitations. Various topologically nontrivial configurations of this confined Clebsch field are responsible for vortex sheets. Stability equations (CVS) for closed vortex surfaces (bubbles of Clebschfield) are derived and investigated. The exact non-compact solution for the stable vortex sheet family is presented. Compact solutions are proven not to exist by De Lellis and Bru. Asymptotic conservation of anomalous dissipation on stable vortex surfaces in the turbulent limit is discovered. We derive an exact formula for this anomalous dissipation as a surface integral of the square of velocity gap times the square root of minus local normal strain. Topologically stable time-dependent solutions, which we call Kelvinons, are introduced. They have a conserved velocity circulation around stationary loop; this makes them responsible for asymptotic PDF tails of velocity circulation, perfectly matching numerical simulations. The loop equation for circulation PDF as functional of the loop shape is derived and studied. This equation is exactly equivalent to the Schrödinger equation in loop space, with viscosity ν playing the role of Planck’s constant. This equivalence opens the way for direct numerical simulation of turbulence on quantum computers. Kelvinons are fixed points of the loop equation at WKB limit ν→ 0. Area law and the asymptotic scaling law for mean circulation at a large area are derived. The representation of the solution of the loop equation in terms of a singular stochastic equation for momentum loop trajectory is presented. 



Review on Turbulence as Clebsch Confinement

When: November 30, 2022 2:00 PM (Israel Standard Time).

Where:  Over Zoom