Pressure Drag of Obstacles in the Atmospheric Boundary Layer

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  • 1 Institut für Meteorologie und Kilmaforschung, Universität/Kernforschungszentrum Karlsruhe, Federal Republic of Germany
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Abstract

Pressure drag of obstacles in the atmospheric boundary layer is computed with a mesoscale numerical model of the troposphere. Different parts of the drag can be separated from the numerical results: total pressure drag is determined from the surface pressure distribution, hydrostatic drag from the temperature distribution in the atmosphere, and form drag as a residual. The dependence of the different parts of the drag on the main influencing parameters, such as geometric parameters, dynamical and thermal parameters, and the surface roughness, is given. The influencing parameters are deduced from a scale analysis of the equation of motion. Wave drag due to gravity waves and flow separation will not be considered in this paper.

The study shows among other points that there is a surface Rossby number similarity for form drag on smooth obstacles, that there may be wave drag due to inertial waves even for neutral or unstable stratification due to inertial waves, and that there is Reynolds number similarity for form drag only with respect to molecular viscosity and not with respect to turbulent viscosity of the air. The results suggest the separation of form drag into two parts: a viscous form drag due to turbulent viscosity of the air, and a turbulent form drag due to additional production of turbulence in the vicinity (mainly in the Ice) of the obstacle. The distinction of different drag producing mechanisms will help in the task of parameterization.

Parameterization using similarity theories is meaningful only for ensembles of obstacles. Here, isolated obstacles are considered for simplicity, therefore, only the prerequisites for the parameterization are discussed in this paper. The main result is that parameterization of pressure drag in terms of an effective roughness length using Rossby number similarity theory will be possible only for the two parts of the form drag. All other parts of the drag have no corresponding mechanisms in the homogenous boundary layer.

Abstract

Pressure drag of obstacles in the atmospheric boundary layer is computed with a mesoscale numerical model of the troposphere. Different parts of the drag can be separated from the numerical results: total pressure drag is determined from the surface pressure distribution, hydrostatic drag from the temperature distribution in the atmosphere, and form drag as a residual. The dependence of the different parts of the drag on the main influencing parameters, such as geometric parameters, dynamical and thermal parameters, and the surface roughness, is given. The influencing parameters are deduced from a scale analysis of the equation of motion. Wave drag due to gravity waves and flow separation will not be considered in this paper.

The study shows among other points that there is a surface Rossby number similarity for form drag on smooth obstacles, that there may be wave drag due to inertial waves even for neutral or unstable stratification due to inertial waves, and that there is Reynolds number similarity for form drag only with respect to molecular viscosity and not with respect to turbulent viscosity of the air. The results suggest the separation of form drag into two parts: a viscous form drag due to turbulent viscosity of the air, and a turbulent form drag due to additional production of turbulence in the vicinity (mainly in the Ice) of the obstacle. The distinction of different drag producing mechanisms will help in the task of parameterization.

Parameterization using similarity theories is meaningful only for ensembles of obstacles. Here, isolated obstacles are considered for simplicity, therefore, only the prerequisites for the parameterization are discussed in this paper. The main result is that parameterization of pressure drag in terms of an effective roughness length using Rossby number similarity theory will be possible only for the two parts of the form drag. All other parts of the drag have no corresponding mechanisms in the homogenous boundary layer.

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