Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2008-01-19
E. Gkioulekas (2008): Phys. Rev. E 78, 066302
Nonlinear Sciences
Chaotic Dynamics
v2: 23 pages; 4 figures; minor revisions; resubmitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.78.066302
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 non-perturbative 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.
No associations
LandOfFree
Locality and stability of the cascades of two-dimensional turbulence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Locality and stability of the cascades of two-dimensional turbulence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Locality and stability of the cascades of two-dimensional turbulence will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-18705