Rossby number similarity of an atmospheric RANS model using limited-length-scale turbulence closures extended to unstable stratification

The design of wind turbines and wind farms can be improved by increasing the accuracy of the inflow models representing the atmospheric boundary layer. In this work we employ one-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations of the idealized atmospheric boundary layer (ABL), using turbulence closures with a length-scale limiter. These models can represent the mean effects of surface roughness, Coriolis force, limited ABL depth, and neutral and stable atmospheric conditions using four input parameters: the roughness length, the Coriolis parameter, a maximum turbulence length, and the geostrophic wind speed. We find a new model-based Rossby similarity, which reduces the four input parameters to two Rossby numbers with different length scales. In addition, we extend the limited-length-scale turbulence models to treat the mean effect of unstable stratification in steady-state simulations. The original and extended turbulence models are compared with historical measurements of meteorological quantities and profiles of the atmospheric boundary layer for different atmospheric stabilities.

Sensitivity studies with different formulations for similarity functions used in surface layer scheme, over the tropical region, in a climate model

<p>The lowest portion of the planetary boundary layer (PBL), where the turbulent fluxes are assumed to be constant, is known as the atmospheric surface layer (ASL). Within the surface layer, the surface exchange processes play an important role in land-atmosphere interaction. Thus, a precise formulation of the surface fluxes is crucial to ensure an adequate atmospheric evolution by numerical models. The Monin–Obukhov Similarity Theory (MOST) is a widely used framework to estimate the surface turbulent fluxes within the surface layer. MOST uses similarity functions of momentum (φ<sub>m</sub>) and heat (φ<sub>h</sub>) for non-dimensional wind and temperature profiles. Over the years, various formulations for these similarity functions have been proposed by the researchers ranging from linear to non-linear forms. These formulations have limitations in the weak wind, stable, and unstable atmospheric conditions. In the surface layer scheme currently available in the Community Atmosphere Model version 5 (CAM5.0), the stable and unstable regimes are divided into four parts, and the corresponding similarity functions are the functions proposed by Kader and Yaglom (1990) for strong unstable stratification, by Businger et al. (1971) for weak unstable stratification, functions by Dyer (1974) for weak stable stratification, and for moderate to strongly stable stratification, the functions from Holtslag et al. (1990) have been utilized. The criteria used for this classification are somewhat ad-hoc, and there is an abrupt transition between different regimes encountered.            </p><p>       In the present study, an effort has been made to implement the similarity functions proposed by Grachev et al. (2007) for stable conditions and Fairall et al. (1996) for unstable conditions in the surface layer scheme of Community Land Model (CLM) for CAM5.0. In the modified version, the similarity functions for unstable conditions are a combination of commonly used Paulson type expressions for near-neutral stratification and an expression proposed by Carl et al. (1973) that takes in to account highly convective conditions. Similarly, the formulation proposed by Grachev et al., for stable conditions, can cover a wider range of stable stratifications. The simulations with CAM5 model using the existing and modified version of surface layer scheme have been performed with 1° resolution for ten years, and the impact of modified functions on the simulation of various important near-surface variables over the tropical region is analyzed. It is found that the scheme with modified functions improving the simulation of surface variables as compared with the existing scheme over the tropical region. In addition, the limitations arbitrarily imposed on particular variables in the existing surface layer scheme can be eliminated or suppressed by using these modified functions.  </p><p>References:</p><p>Fairall CW, Bradley EF, Rogers DP, Edson JB, Young GS (1996) Bulk parameterization of air-sea fluxes for tropical ocean global atmosphere coupled-ocean atmosphere response experiment. J Geophys Res 101(C2):3747–3764</p><p>Grachev, A.A., Andreas, E.L., Fairall, C.W., Guest, P.S. and Persson, P.O.G. (2007a) SHEBA: flux–profile relationships in stable atmospheric boundary layer. Boundary-Layer Meteorology,124, 315–333.</p><p>Keywords:</p><p>Boundary layer, Turbulence, Climate Model, Surface Fluxes</p>

Rossby number similarity of atmospheric RANS using limited length scale turbulence closures extended to unstable stratification

The design of wind turbines and wind farms can be improved by increasing the accuracy of the inflow models representing the atmospheric boundary layer. In this work we employ one-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations of the idealized atmospheric boundary layer (ABL), using turbulence closures with a length scale limiter. These models can represent the mean effects of surface roughness, Coriolis force, limited ABL depth, and neutral and stable atmospheric conditions using four input parameters: the roughness length, the Coriolis parameter, a maximum turbulence length, and the geostrophic wind speed. We find a new model-based Rossby similarity, which reduces the four input parameters to two Rossby numbers with different length scales. In addition, we extend the limited length scale turbulence models to treat the mean effect of unstable stratification in steady-state simulations. The original and extended turbulence models are compared with historical measurements of meteorological quantities and profiles of the atmospheric boundary layer for different atmospheric stabilities.