On numerical realizability of thermal convection

Astounded at the regularity of convective structures observed in simulations of mesoscale flow past realistic topography, we take a deeper look into numerics of a classical problem of flow over a heated plate [1]. We find that solutions are sensitive to viscosity, which is either incorporated a priori or effectively realized in numerical models. In particular, anisotropic viscosity can lead to regular convective structures [2,3,4] that mimic naturally realizable Rayleigh-Benard cells that are, however, unphysical for the specified external parameter range. The details of the viscosity appear to play secondary role; that is, similar structures can occur for prescribed constant viscosities, explicit subgrid-scale turbulence models, adhoc numerical filters, or implicit dissipation of numerical schemes. This calls for careful selection of numerical tools suitable for cloudresolving simulations of atmospheric circulations [5].