We performed a numerical simulation of penetrative convection of an inversion-topped weakly stratified atmospheric boundary layer over urban terrain with a strong localized source of heat and moisture. With some simplifications, the case mimics the real environment of the Krasnoyarsk region in Russia where the non-freezing river Yenisei acts as a thermal and humidity source during winter, generating an undulating fog pattern along the river accompanied with scattered ‘steam devils’. An idealized full diurnal cycle was simulated using an unsteady Reynolds-averaged Navier–Stokes (RANS) three-equation algebraic flux model and the novel buoyancy-accounting functions for treating the ground boundary conditions. The results show a significant effect of the river on the net temperature and moisture distribution. The localized heat and moisture source leads to strong horizontal convection and marked non-uniformity of humidity concentration in the air. An interplay of several distinct large-scale vortex systems leads to a wavy pattern of moisture plumes over the river. The simulations deal with rare natural phenomena and show the capability of the RANS turbulence closure to capture the main features of flow and scalar fields on an affordable, relatively coarse, computational grid.