# Quantum theory of classical turbulence

## 10 am, 5 Dec 2022 – 7 Dec 2022

Over the course of four lectures, Prof. Alexander Migdal will present 35 years of research concerning his new approach to strong turbulence.

In terms of quantum field theory, this is another example of the duality between a fluctuating vector field and fluctuating geometry. He will present new exact solutions of Navier-Stokes and Euler equations and investigate in detail the loop equation suggested in the early 1990s. The loop equation plays the same role in the theory as the Boltzmann kinetic equation in statistical physics. It has the form of the Schrödinger equation with a complex Hamiltonian in loop space. The viscosity plays the role of Planck's constant. Strong turbulence corresponds to the WKB limit of the loop equation.

In this limit, he finds a fixed point of the loop equation he calls Kelvinon. Kelvinon has a conserved circulation for a fixed loop in space, generalising Kelvin's theorem. The Clebsch field of this solution has a nontrivial topology with two winding numbers. These topological conservation laws allow us to compute the PDF of circulation in a WKB limit (large circulation in the viscosity units). This PDF perfectly matches the results of numerical simulations of the conventional forced Navier-Stokes equation.

## Programme

Mon 5 Dec 2022

*10:00*Lecture 1*12:00*Lecture 2

- Wed 7 Dec 2022

*10:00*Lecture 3*12:00*Lecture 4*1:00*Q&A

## Speaker

Professor Alexander Migdal is a senior researcher at New York University. He was formerly at the Landau Institute for Theoretical Physics, the Russian Space Research Institute and Princeton. He currently focuses on loop equations and the field theory of turbulence.