2009/11/27 by Jörg Schumacher, Joerg Schumacher, Bruno Eckhardt +1
Earth and Planetary Sciences · Engineering · Environmental Science · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Plant Water Relations and Carbon Dynamics #physics.flu-dyn
paper · pdf · doi:10.1016/j.physleta.2009.11.078
published as Phys. Lett. A, 374 (2010) 861 · 12 pages, 5 Postscript figures, accepted for publication in Physics Letters A
arxiv created 2009/11/27 · openalex publication_date 2009/12/07 · arxiv updated 2010/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
According to statistical turbulence theory, the ensemble averaged squared vorticity rhoE is expected to grow not faster than drhoE/dt ~ rhoE3/2. Solving a variational problem for maximal bulk enstrophy (E) growth, velocity fields were found for which the growth rate is as large as dE/dt ~ E3. Using numerical simulations with well resolved small scales and a quasi-Lagrangian advection to track fluid subvolumes with rapidly growing vorticity, we study spatially resolved statistics of vorticity growth. We find that the volume ensemble averaged growth bound is satisfied locally to a remarkable degree of accuracy. Elements with dE/dt ~ E3 can also be identified, but their growth tends to be replaced by the ensemble-averaged law when the intensities become too large.