Large eddy simulation of a weakly stable boundary layer using dynamic subgrid-scale models

The stable boundary layer is studied numerically using large eddy simulation (LES) in conjunction with dynamic subgrid-scale models. A classical dynamic Smagorinsky model (Germano et al., 1991) for the boundary layer interior is blended together with a mean eddy viscosity prescription for the near-surface region (Sullivan et al., 1994). Aside from relying on Monin-Oboukhov (M.-O.) similarity theory for the near-surface region, this approach leads to parameter-free estimation of the eddy viscosity and eddy diffusivity. The effects of stability are accounted for automatically, obviating the need for ad hoc stability corrections or for a parameterization of the turbulent Prandtl number.

The weakly-stable boundary layer case of Kosovic and Curry (2000) is used as the basis for the simulations and these are part of the ongoing GEWEX Atmospheric Boundary Layer Study (GABLS). Results are generated on meshes containing 64X64X64, 130X130X136, and 200X200X216 points. For each mesh resolution, three separate subgrid-scale models are used. These are: (1) the dynamic Smagorinsky model with the near-surface treatment discussed above, (2) a dynamic Smagorinsky model without special near-surface treatment, and (3) the turbulent kinetic energy (tke) eddy viscosity model with near-surface treatment of Sullivan et al. (1994). The simulations are carried out for nine hours of physical time and statistics are sampled over the last hour. The flow fields are observed to be continuously turbulent and reach a quasi stationary state after about five hours of evolution. Both models with special near-surface treatment produce results that are in good agreement with M.-O. similarity theory. The pure dynamic model, on the other hand, produces anomalous results where the turbulent fluctuations are overpredicted near the surface and agreement with similarity theory is poor. This finding illustrates the need to modify the subgrid-scale parameterization very near the surface where the turbulence is necessarily under resolved in stable conditions.

The three separate meshes are used to perform a convergence study. It is found that the integral quantities such as boundary layer thickness, M.-O. length, surface drag, and surface heat flux vary continuously as the mesh is refined. This result implies that extremely fine meshes must be used in order to achieve definitive LES results of the stable boundary layer.

The results from the dynamic model simulation with the near-surface treatment, computed on the 200X200X216 mesh, are used to assess the accuracy of some aspects of mesoscale turbulence parameterizations. The LES data indicates that the stability functions commonly used to suppress mixing under stable conditions should decrease more rapidly with Richardson number and a new stability function having this behavior is suggested. The LES data is also used to estimate the mixing length and this is compared with a few common parameterizations used in mesoscale modeling.

REFERENCES

Germano, M., U. Piomelli, P. Moin, and W. H. Cabot: 1991, `A dynamic subgrid-scale eddy viscosity model'. Phys. Fluids A 3, 1760--1770.

Sullivan, P. P., J. C. McWilliams, and C.-H. Moeng: 1994, `A Subgrid-Scale Model For Large-Eddy Simulation of Planetary Boundary-Layer Flows'. Boundary-Layer Meteorol. 71, 247--276.

Kosovic, B. and J. A. Curry: 2000, `A Large-Eddy Simulation Study of A Quasi-Steady Stably-Stratified Atmospheric Boundary Layer'. J. Atmos Sci. 57, 1052--1068.