On the Local Structure of Two-Dimensional Turbulence

Abstract

Possible consequences of the application of the Kolmogorov theory of local isotropy to two-dimensional turbulence are discussed. In this regard, the cases of both freely decaying and stationary turbulence are considered. Formulae for the third-order structure functions in the inertial interval are obtained as the solutions of the Karman—Howarth equation with the use of the well-known relation between the velocity and vorticity correlators. These formulae differ from those given by other authors; that is, the variable term linear in space turns out to be negative in the corresponding formula, as in the three-dimensional case. The possible relation of the results to the form of the energy spectrum is briefly mentioned.