Application of Reynolds' stress closure to the stable boundary layer
A new turbulence closure scheme has been implemented in the National Taiwan University-Purdue University Non-hydrostatic model for the purpose of simulating the planetary boundary layer under strong, stable stratification. Under such stratification, turbulent motions may develop but will exhibit characteristics that make current modeling methods unsuitable. To overcome modeling difficulties posed by the lack of quasi-equilibrium, isotropic turbulence, a new scheme has been developed, which solves the higher-order turbulent transport equations rather than modeling the turbulent fluxes directly. The model was tested using three idealized simulations. The first simulation successfully generated and maintained Kelvin-Helmholtz waves in a thin shear layer. The new scheme showed significantly weaker turbulent fluxes than the single-equation eddy-viscosity closure scheme used previously in the model. The second simulation involved flow around a bell-shaped mountain with low Froude number. Strong counter rotating vortices developed on the lee side of the mountain, maintaining their structure for the entire simulation. This contrasts with the simulation using the eddy-viscosity scheme, which produced much weaker vortices that continued to weaken over time instead of reaching a quasi-steady state. The third simulation involved a high Froude number situation over a bell-shaped mountain, and produced non-linear mountain waves, a strong hydraulic jump and a surface-wind maximum in-excess of twice the free-stream velocity. The new scheme showed significantly smaller turbulent fluxes and the ability to maintain gradients in the flow fields better than the eddy-viscosity model. However, greater numerical smoothing was needed to avoid instability, and the scheme increases computational requirements significantly. The new model is a promising new tool for investigating phenomena that require more detailed physics and higher resolutions, without needing to resort to direct numerical simulation, but may not be worth the cost for simulations involving large scale forcing or the generation of more slowly varying structures. ^
Wen-Yih Sun, Purdue University.