2017/10/31 by Olivier Poujade, Poujade, Olivier
Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.1710.11378
openalex publication_date 2017/10/31 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
Theoretical developments in the field of Lagrangian turbulence are made\ndifficult by the fact that equations governing the evolution of lagrangian\nflows are implicit contrary to eulerian flows. In this article, an it exact\nexplicit equation for incompressible lagrangian fluid flows at high-Reynolds\nnumber is constructed. The method to arrive at the equation of motion and the\nproof that it describes the motion of an incompressible fluid are provided. A\ntruncated version of this new equation is used to show how the lagrangian\nturbulent spectrum (E_\lag(\ω)) could be inferred. This exercise\nshowed a complex interrelation between the stirring force field and the flow\nitself in the lagrangian turbulence framework whereas the stirring is not\naffected by the flow in the eulerian point of view. The result is that\nE_\lag(\ω)\∝ \ε ,\ω-2 seems independent upon\nthe way the fluid is stirred in the inertial range for a given dissipated power\n\ε. It also showed that E_\lag(\ω)\∼ \ω-s\nwith 0\≤ s\≤ 1/2 (depending on the stirring) at low-\ω and\n\∼\ω-4 in the viscous range at high-\ω.\n