Locality and stability of the cascades of two-dimensional turbulence

Authors

Eleftherios Gkioulekas, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

12-4-2008

Abstract

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.

Comments

© 2008 American Physical Society. Original published version available at https://doi.org/10.1103/PhysRevE.78.066302

Recommended Citation

Gkioulekas, Eleftherios. "Locality and stability of the cascades of two-dimensional turbulence." Physical Review E 78.6 (2008): 066302. https://doi.org/10.1103/PhysRevE.78.066302

Publication Title

Physical Review E

DOI

10.1103/PhysRevE.78.066302