Large-eddy simulations of radiatively driven convection: Sensitivities to the representation of small scales

Large-eddy simulations of a smoke cloud are examined with respect to their sensitivity to small scales as manifest in either the grid spacing or the subgrid-scale (SGS) model. Calculations based on a Smagorinsky SGS model are found to be more sensitive to the effective resolution of the simulation than are calculations based on the prognostic turbulent kinetic energy (TKE) SGS model. The difference between calculations based on the two SGS models is attributed to the advective transport, diffusive transport, and/or time-rate-of-change terms in the TKE equation. These terms are found to be leading order in the entrainment zone and allow the SGS TKE to behave in a way that tends to compensate for changes that result in larger or smaller resolved scale entrainment fluxes. This compensating behavior of the SGS TKE model is attributed to the fact that changes that reduce the resolved entrainment flux (viz., values of the eddy viscosity in the upper part of the PBL) simultaneously tend to increase the buoyant production of SGS TKE in the radiatively destabilized portion of the smoke cloud. Increased production of SGS TKE in this region then leads to increased amounts of transported, or fossil, SGS TKE in the entrainment zone itself, which in turn leads to compensating increases in the SGS entrainment fluxes. In the Smagorinsky model, the absence of a direct connection between SGS TKE in the entrainment and radiatively destabilized zones prevents this compensating mechanism from being active, and thus leads to calculations whose entrainment rate sensitivities as a whole reflect the sensitivities of the resolved-scale fluxes to values of upper PBL eddy viscosities.