Simulation of an evolving convective boundary layer using a scale-dependent dynamic Smagorinsky model at near grey-zone resolutions

Abstract

A scale-dependent Lagrangian-averaged Dynamic Smagorinsky sub-grid scheme with stratification effects is used to simulate the evolving convective boundary layer of the Wangara case study in the grey-zone regime (specifically, for grid lengths from 25 to 400 m). The dynamic Smagorinsky and standard Smagorinsky approaches are assessed for first and second order quantities in comparison with results derived from coarse-grained LES fields. In the LES regime the sub-grid schemes produce very similar results, albeit with some modest differences near the surface. At coarser resolutions, the use of the standard Smagorinsky significantly delays the onset of resolved turbulence, the delay increasing with coarsening resolution. In contrast, the dynamic Smagorinsky scheme much improves the spin-up and so is also able to maintain consistency with the LES temperature profiles at the coarser resolutions. Moreover, the resolved part of the turbulence reproduces well the turbulence profiles obtained from the coarse-grained fields, especially in the near grey-zone. The dynamic scheme does become somewhat over-energetic with further coarsening of the resolution, especially near the surface. The dynamic scheme reaches its limit in our current configuration when the test filter starts to sample at the unresolved scales returning very small Smagorinsky coefficients. Sensitivity tests reveal that the dynamic model can adapt to changes in the imposed numerical or sub-grid diffusion by adjusting the Smagorinsky constant to the changing flow field and minimising the dissipation effects on the resolved turbulence structures