Intrigued by the regularity of convective structures observed in simulations of mesoscale flow past realistic topography, we take a deeper look into computational aspects of a classical problem of the flow over a heated plane. We find that the numerical solutions are sensitive to viscosity, either incorporated a priori or effectively realized in computational models. In particular, anisotropic viscosity can lead to regular convective structures that mimic naturally realizable Rayleigh-Bénard (RB) cells but are unphysical for the problem at hand. This is becoming important since the advent of “cloud resolving” numerical weather prediction (NWP) [1, 2] and a rapid progress towards the petascale computing. Even with a relatively fine (for NWP) horizontal resolution δ ~ O(103) m numerical filtering is practically unavoidable [2], hence the simulated convection remains grossly under-resolved. The linear theory [3, 4] shows that anisotropic viscosity (characteristic of under-resolved NWP) modifies the range of unstable classical RB modes [5]. In particular, for an effective viscosity much larger in the horizontal than in the vertical unphysically broad RB cells may be observed.