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.
Participants
Klas Modin (contact)
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Funding
Swedish Research Council (VR)
Project ID: 2022-03453
Funding Chalmers participation during 2023–2026