| The breakthrough in the Kraichnan model of a scalar $\theta$ advected and pumped respectively by two prescribed independent identical Gaussian fields with short- ($\delta$-)correlation in time has been illuminating but is far from solving the full problem of passive scalar turbulence. The relevant progresses and challenges can be found in the typical reviews such as G. Falkovich, K. Gaw\c{e}dzki \& M. Vergasolla. \textit{Rev. Mod. Phys.} {\bf 73}: 913--975, 2001, and, A. Celani, M. Cencini, A. Mazzino and M. Vergassola. \textit{New Journal of Physics} {\bf 6}: 00, 2004. Here we discuss the full problem with self-consistent (dynamical) incompressible two-dimensional (2D) advecting velocity $\bm{v}$ and with the dependence of the pumping $f_{\theta}$ on the vorticity $\bm{\omega}=\nabla\times\bm{v}$. We discuss, with logical reasoning from active scalar turbulence results and with absolute equilibrium statistics constrained by the the cross-correlation $\mathcal{C}=\langle \theta\omega \rangle$, the new physical aspects, especially the indication of possible non-universality of the 2D passive scalar transfers: Even the transfer/cascade directions of the passive scalar may depend on the mechanisms of $f_{\theta}$. A modification of Kraichnan model by imposing linear dependence of $f_{\theta}$ on $\bm{\omega}$ is preliminary discussed. |