Abstract: The nonequilibrium statistical-mechanics theory of a passive scalar field convected by turbulence is applied to study the variance spectrum G(k) of a 2-D (two-dimensional) turbulent passive scalar field in the convective range, while the velocity spectrum E(k)= cX2/3k-3 in the enstrophy cascade range, here X is the enstrophy dissipation rate, C is a dimensionless coefficient. The closure equations in this case are divergent due to the nonlocalness of the cascade process in 2-D turbulence. In order to overco...