Direct and Large-Eddy simulations of stable boundary layers: turbulent kinetic energy and flux budgets

Understanding and parameterizing turbulent fluxes in statically stable boundary layers, where buoyant forces destroy turbulent kinetic energy remains a challenging, yet very important problem in geophysical fluid dynamics. Numerical simulations, with their ability to provide 3D, time-varying information on turbulent structures and dynamics are increasingly used to tackle the problem. However, some uncertainties regarding the performance of various flow simulation techniques remain, especially under highly stable conditions where turbulence can be globally or locally suppressed. For Large Eddy Simulations (LES), strongly stable cases remain challenging for two reasons. First, due to strong stratification there is reduction in size of the eddies; this reduces the fraction of the turbulent kinetic energy that the simulation can resolve and the resolution with which the most energetic eddies are captured, and could lead to an increased importance of the subgrid scales and models outside of the surface layer. Second, under strongly stable conditions turbulence can become spatially intermittent resulting in inhomogeneity in turbulence fields, and invalidating some assumptions often used in numerical models. To better understand these limitations in LES and to improve current models under strongly stable conditions, we perform a series of direct and large-eddy numerical simulations under moderate Reynolds numbers, with the aims of 1) validating LES results under strongly stable conditions, and 2) investigating the effect of stability on TKE and flux budgets. Our results indicate that the effect of stability is mostly seen in the TKE production term. Changes in the vertical profile of TKE production are significant when the surface Richardson number is increased from 0 to 0.001, but with further increase, they are less pronounced. Direct buoyancy destruction though non-zero, is negligible. This implies that there is some other mechanism by which stability affects the flow field. To investigate this, we examined quantities involved in TKE production, namely the gradients and fluxes. We observe that gradients are almost the same in both cases, except near the wall. On the other hand, turbulent fluxes are damped significantly. Analysis of flux budget shows that quantities that are most affected by stratification are pressure diffusion and pressure strain. Turbulent diffusion are also significantly reduced, suggesting dampening of vertical motions due to buoyancy.