2008/01/31 by Eleftherios Gkioulekas · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Cascade #Computer science #Dissipation #Energy cascade #Enstrophy #Fluid Dynamics and Turbulent Flows #Forcing (mathematics) #Geometry #Inverse #Locality #Mathematical analysis #Mathematics #Mechanics #Phase Equilibria and Thermodynamics #Physics #Quantum mechanics #Stability (learning theory) #Statistical physics #Turbulence #nlin.CD
paper · pdf · doi:10.1103/physreve.78.066302
published as E. Gkioulekas (2008): Phys. Rev. E 78, 066302 · v2: 23 pages; 4 figures; minor revisions; resubmitted to Phys. Rev. E
arxiv created 2008/09/14 · openalex publication_date 2008/12/04 · arxiv updated 2010/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L'vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade. For the enstrophy cascade, statistical stability requires large-scale dissipation and a vanishing downscale energy dissipation. A careful discussion of the subtle notion of locality is given at the end of the paper.