Long-time 2D hydrodynamics via quantization

Research Project, 2023 – 2026

Characterization of the long-time behavior of an inviscid incompressible fluid evolving on a closed 2D domain is a long-standing problem in mathematics and physics. The motion is described by Euler’s equations: a non-linear system with infinitely many conservations laws, yet non-integrable dynamics. In both experiments and numerical simulations, coherent vortex structures typically form after some stage of initial mixing. These formations dominate the slow, large-scale dynamics. Nevertheless, fast, small-scale dynamics also persist. To rigorously understand this separation of scales is the essence of 2D turbulence. In this project I use quantization theory to enable mathematical tools for addressing the scale separation. Central to the idea is a new, canonical splitting of the quantized vorticity which evolves into a separation of scales, thus providing quantitative dynamics for scale separation in the quantized regime. I shall spend 50% of my time in the project. In addition, one post-doc and one PhD student will spend all their research in the project.