2023/10/02 by Giorgio Krstulovic, Sergey Nazarenko, Krstulovic, Giorgio +1 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2310.01121
openalex publication_date 2023/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study numerically the temporal evolution of an initially random large-scale velocity field under governed by the hyperviscous incompressible Navier-Stoke equations. Three stages are clearly observed during the evolution. First, the initial condition development is characterized by a spectrum evolving in a self-similar way with a wave number front k_*(t) propagating toward high values exponentially in time. This evolution corresponds to the formation and shrinking of think vortex pancakes exponentially in time, as it has been previously reported in simulations of the incompressible Euler equations. At the second stage, pancakes become unstable, rolling up on the edges and breaking up in the middle, leading to the emergence of vortex ribs -- quasi-periodic arrangements of vortex filaments. Those filaments then twist creating structures akin to ropes. At the last stage, a fully developed turbulent state is observed, characterized by a Kolmogorov energy spectrum and exhibiting a decay law compatible with standard turbulent predictions in the case of an integral scale saturated at the scale of the box.