On the properties of decaying two-dimensional turbulence: Characteristic features of the spectra and coherent structures

Abstract

The main results of the theory of two-dimensional turbulence are presented. The conventional approach based on the Karman-Howarth equation is used to describe anomalous properties (sharply differing from those inherent in usual three-dimensional turbulence) of two-dimensional turbulent motion of an incompressible fluid, in particular, energy transfer across the spectrum from larger toward smaller wave numbers and the formation of coherent structures, whose origin is associated with the fact that the spectrum attains the form of a δ-function. A uniform method is proposed for obtaining self-similar spectra of two-dimensional turbulence in inertial ranges. The problem of turbulent diffusion of a passive tracer in the two-dimensional case is also considered. It turns out that the corresponding quantities, as well as those related to the dynamic characteristics of motion, can exhibit anomalous properties under certain conditions. The relationship between the results and experimental data is discussed. In particular, the experimentally observed inversion of the spectra of two-dimensional turbulence in the atmosphere is explained.