On the Reynolds stresses in mean-field hydrodynamics II. Two-dimensional turbulence and the problem of negative viscosity

The methods proposed in a foregoing paper are used for the derivation of the eddy viscosity of a two-dimensional homogeneous isotropic turbulence. In contrast to three-dimensional isotropic turbulence is shown that for the two-dimensional case the eddy viscosity (i) has no definite sign, (ii) tends to zero if the molecular viscosity tends to zero, (iii) is negative for special cases. However, the modes with large wave numbers decay in any case as is shown by investigating a dispersion relation.