Abstract:

This work provides analytical results of the two-dimensional Karman-Howarth equation. A self-similar decay of two-dimensional turbulence energy spectrum has also been determined. These expressions are a counterpart of three-dimensional turbulence. The behavior of the inverse energy cascade in a two-dimensional isotropic homogeneous turbulence can be understood from the view point of present statistical solution. 

Key words:  two-dimensional isotropic homogeneous turbulence; Karman-Howarth equation; exact solution; inverse energy cascade