Organized by:
Theodore Drivas (Stony Brook)
Gregory Falkovich (Weizmann)
Vladimir Rosenhaus (CUNY)
Vlad Vicol (NYU)
The last decade has seen significant progress in the studies of turbulence, understood widely as a far-from-equilibrium state of a system with many degrees of freedom. This is due, in particular, to the two just-finished Simons collaborations, one on wave turbulence and another on the statistical physics approach to fluid turbulence. A rich set of physical results, both experimental and theoretical, has been obtained along with fast progress in mathematical methods and rigorous results. While there is no lack in conferences and workshops on different aspects of turbulence, it is high time for people from all fields and corners of turbulence research to get together for a longer stay in a more relaxed setting. There are several new things that are worth discussing in a multi-disciplinary context.
Among the new things is the dramatic advance in wave turbulence in three directions. First, there is an abundance of new experimental and numerical data on turbulence in laboratory, geophysical, and astrophysical systems. Second, there is significant progress in rigorous mathematical proofs of the validity domain of wave kinetic equations and weak turbulence theory. Third, there is a long-awaited revival of applying the methods of quantum field theory to wave turbulence, which allows progress from weak to strong turbulence in analytic theory. That also opens new venues for identifying universality classes of wave-turbulence systems. That opens wide possibilities for future progress in analytical description and calls for tight collaboration with experiments (natural and numerical) to test the recent predictions and present new challenges for the theory.
On classical fluid turbulence, there are many new surprising experimental results obtained during the last decade, particularly on boundary layers and pipe flows, which deserve to be properly discussed and internalized by theoretical physicists and mathematicians. Here, too, we may be in for realizing that there could be several classes of high-Reynolds-number incompressible turbulence rather than a single “Kolmogorov turbulence.”
On the mathematical side, there has been a good deal of progress recently in understanding the formation of singularities, and the non-uniqueness of weak solutions. For instance, it is now known that classical solutions of the Euler equation can form a singularity in finite time, and that weak solutions of forced Euler with unbounded but p-integrable vorticity may be non-unique. This later result holds also for Leray weak solutions of Navier-Stokes equation. Physically, these non-uniquness results shed light on Eulerian spontaneous stochasticity in fluid systems. In addition, there has been much activity in understanding anomalous dissipation/diffusion in “turbulent” toy models, such as passive scalar advection. Non-smooth and multiscale constructions resembling inertial range dynamics give a new, constructive perspective on Lagrangian spontaneous stochasticity and its implications for scalar turbulence.
In formal quantum field theory, there has been growing recognition of the importance of studying richer sets of field theories, such as those lacking Lorentz invariance, as well as states in field theory that are far from the vacuum, such as e.g. the large charge expansion. In more applied quantum field theory contexts, the past decade has seen significant activity— both in condensed matter and high energy theory communities — in studying quantum field theory in states that are far from equilibrium. Notably, wave turbulence in this context has been studied in QCD, in the aftermath of a hadron collision. Separately, the past two decades have witnessed the study of relativistic fluids, again arising from hadron collisions.
Some of the mini-course topics for this event include:
1. Physics of turbulence
2. Mathematics of turbulence
3. Field theory of turbulence
This program is associated with the workshop: Physics and mathematics of turbulence in different media: September 14-18, 2026