On isotropic two-dimensional turbulence

Correlations between space rates of change of velocities and an expression for the time mean dissipation of turbulent energy are derived for two-dimensional isotropic turbulence following Taylor, who derived parallel relationships for three dimensions. Definite differences occur that lead to simple interpretation. The von Karman equation for correlation of velocity components in various directions shows that the Taylor length scale is always zero for two-dimensional turbulence, which indicates that the Taylor definition of the average eddy size may not have real significance, at least for two-dimensional turbulence.