Locality of turbulent cascades

In this paper we establish sufficient conditions for locality of turbulent cascades, by an exact analysis of the fluid equations. No assumptions of homogeneity or isotropy are invoked and the results apply to individual realizations with no resort to any statistical averaging. The only requirement is suitable regularity of the turbulent solutions of the fluid equations in the high Reynolds number limit, corresponding to Holder continuity but non-differentiability in space. We use a smooth filtering approach to resolve the turbulent fields both in space and in scale. We discuss several physical cascades to exemplify and clarify the analysis, including joint energy and helicity cascades in three space dimensions and the dual inverse energy cascade and direct enstrophy cascade in two dimensions. (c) 2005 Elsevier B.V. All rights reserved.