The Eulerian models of the dispersal of a passive air pollutant are formulated. Those are the high-order closure model of the dispersal, in which the concentration fluxes <uic> are calculated by the transport equations (DC-model), and the algebraic model of turbulent fluxes <uij> (AC-model) obtained by simplification of the DC-model to the algebraic expressions in the approximation of weak-equilibrium turbulence. Both of the models use the mean wind and turbulence values from the second-order closure model of the atmospheric boundary layer (the three-parameter E- e - <q2> turbulence model). The basic characteristics of the thermohydrodynamic fields of a turbulent thermal plume above an urban heat island are reproduced by the E- e - <q2> model in quite a good agreement with the experimental data and in situ measurements of the turbulence intensity. Calculated results on the dispersal of a passive pollutant from the surface source obtained by use of the DC and AC models show that the maximum difference in the concentration near the source does not exceed ten percent. Besides, it is shown that diffusion terms of the DC-models, excluded while obtaining the AC-model, act to smooth out flux gradients. The verification performed demonstrated the validity of using the algebraic AC-model in practice of simulating the atmospheric pollutants dispersal.