Modeling subgrid-scale heat fluxes in the neutral and stratified atmospheric boundary layer

Abstract

The performances of four models for the subgrid-scale heat flux under conditions of poor resolution typical of large-eddy simulation of atmospheric boundary layer flows are compared using observational data. It is argued that a key feature of a numerically stable model is to accurately predict the probability density function of the dissipation of resolved temperature variance (or at least not overpredict the amount of backscatter). The results show that the nonlinear model yields excessive backscatter in agreement with numerical instabilities observed in a posteriori implementations. It is also observed that the Daly–Harlow–Smagorinsky model performs much better, despite having a similar structure. The source of the excessive backscatter in the nonlinear model is tracked to the presence of the rotation component in the tensor eddy diffusivity. A modified version of the Daly–Harlow model is proposed on the basis of a closure for the subgrid-scale stress tensor using the nonlinear model after elimination of the rotation effects.

Keywords:

• atmospheric turbulence
• large-eddy simulation
• turbulence modeling: subgrid scale
• heat flux

Acknowledgements

Horizontal Array Turbulence Study measurements were made by the National Center for Atmospheric Research's Integrated Surface Flux Facility.

Notes

1. Although the Smagorinsky model does not allow for backscatter of the square-resolved temperature ⟨ ⟩, it does allow for backscatter of resolved variance σ_θ: if (q ^smag )″= -Pr _sgs ⁻¹(C _s Δ)²(||∇)″ is used in Equation (9), one gets χ∝(||∇)″·∇()″;, which can be locally negative.