Physics Colloquium / talk by Prof. Alexander Migdal

Decoding fluid chaos: The arithmetic attractor of decaying turbulence

Abstract:

Turbulence is often described as the last great unsolved problem of classical physics. In this colloquium I will review a line of work suggesting that, at least for decaying turbulence, the apparent disorder hides a surprisingly rigid underlying structure. The starting point is a reformulation of the Navier–Stokes dynamics in loop space, where the nonlinear evolution of the fluid is recast in terms of circulation loops rather than the velocity field itself. In this language, the late-time turbulent state admits an exact decaying solution in terms of a one-dimensional momentum loop.
The striking feature of this solution is that its support is not organized by a smooth continuum, as in standard multifractal pictures, but by reduced rational numbers. In the continuum limit, these rational data become dense and generate what I call an arithmetic attractor: a singular geometric object whose intermittency is encoded by number-theoretic structure, specifically the Farey sequence of coprime fractions. I will explain this idea in nontechnical terms and show how it leads to a new interpretation of fluid chaos, in which randomness at large scales is organized by a hidden deterministic arithmetic skeleton.
I will also discuss recent large-scale numerical simulations showing that very different randomized initial conditions converge, in the bulk, toward the same predicted behavior. This supports the view that the Euler ensemble describes a universal late-time state of decaying turbulence. More broadly, the talk will present loop-space methods, developed over decades in gauge theory and now extended to fluids, as a new language for nonlinear dynamics that has already opened several longstanding nonlinear problems in classical and quantum physics to exact analysis.

About the speaker:

Professor Alexander A. Migdal is a distinguished theoretical physicist working at IAS Princeton whose career has spanned foundational on anomalous dimensions and conformal bootstrap methods, and made major advances in large-𝑁𝑁 QCD, loop equations, and two-dimensional quantum gravity. After a successful transition to industry as an inventor, entrepreneur, and technology leader, Professor Migdal returned to academia in 2019 as a Research Professor at NYU. Since then, he has developed a bold new framework for turbulence, including exact analytic solutions of Navier–Stokes loop equations and striking connections between classical turbulence, quantum mechanics, and number theory. His recent work challenges long-standing assumptions in turbulence theory and has attracted international attention. He is currently a Distinguished Visitor at IAS Luxembourg, hosted by the TopTurbQC project led by Professors Adolfo del Campo and Jean-Marc Schlenker.

Spring Physics Colloquium will follow a new format:

• The colloquium will take place on Monday, 27 April , at 1:00 PM in room BSC 2.01 in the Bâtiment des Sciences at Campus Limpertsberg;
• Before the colloquium, we warmly invite you to a lunch break at 12:00 PM in the main hall of the Bâtiment des Sciences. This is a great opportunity to engage with Prof. Alexander A. Midgal and connect with fellow attendees over a nice coffee break. For logistics purposes, please register by Friday, 24 April, using the Coffee registration link below;
• Attendance in person is preferred. If you are unable to join us in person, you can still participate in the event remotely through the Webex link provided below. Meeting number (access code): 2783 097 4784; Meeting password: HWwsJqew394.

• Lunch registration
• Webex link