Local and Nonlocal Transfer of Motion Integrals in Wave Turbulence

Abstract

The picture of cascade turbulence suggested by Richardson, Kolmogorov and Obukhov is based on the concept of interaction locality [1–5]. That means that those modes (vortices or waves) effectively interact which are of comparable scales only. The question naturally arise: whether a locality property should be satisfied on the steady Kolmogorov-like spectrum only or on the slightly differing distributions as well? Proceeding from continuity-like speculations, one might suppose that in general case interaction locality for Kolmogorov distribution leads to that for close ones. Such a supposition is, however, incorrect since Kolmogorov spectrum usually possesses higher degree of symmetry (for example, being isotropic) than arbitrary yet close distributions. A stationary locality does not mean thus an evolutionary locality as it was stated in [4,6].