2013/12/23 by F. Spineanu, Florin Spineanu, M. Vlad +3
Engineering · Environmental Science · Physics and Astronomy · #Climate variability and models #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Phase Equilibria and Thermodynamics #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1312.6613
2D Euler dynamics in Field Theory, in the asymptotic regime: very detailed calculations (114 pages); more explanations added to Introduction, Discussion
openalex publication_date 2013/12/23 · arxiv created 2014/09/18 · arxiv updated 2014/09/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The ideal incompressible fluid in two dimensions (Euler fluid) evolves at relaxation from turbulent states to highly coherent states of flow. For the case of double spatial periodicity and zero total vorticity it is known that the streamfunction verifies the sinh-Poisson equation. These exceptional states can only be identified in a description based on the extremum of an action functional. Starting from the discrete model of interacting point-like vortices it was possible to write a Lagrangian in terms of a matter function and a gauge potential. They provide a dual representation of the same physical object, the vorticity. This classical field theory identifies the stationary, coherent, states of the 2D Euler fluid as derived from the self-duality. We first provide a more detailed analysis of this model, including a comparison with the approach based on the statistical physics of point-like vortices. The second main objective is the study of the dynamics in close proximity of the stationary self-dual state, i.e. before the system has reached the absolute extremum of the action functional. Finally, limitations and possible extensions of this field theoretical model for the 2D fluids model are discussed and some possible applications are mentioned.