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The Local Structure of Atmospheric Turbulence and Its Effect on the Smagorinsky Model for Large Eddy Simulation

Marcelo ChameckiDepartment of Geography and Environmental Engineering, and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, Maryland

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Charles MeneveauDepartment of Mechanical Engineering, and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, Baltimore, Maryland

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Marc B. ParlangeSchool of Architecture, Civil, and Environmental Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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Abstract

Phenomena such as large-scale shear, buoyancy, and the proximity to the ground surface significantly affect interactions among scales in atmospheric boundary layer turbulent flows. Hence, these phenomena impact parameters that enter subgrid-scale (SGS) parameterizations used in large eddy simulations (LES) of the atmospheric boundary layer. The effects of these phenomena upon SGS parameters have, to date, been studied mostly as functions of the global state of the flow. For instance, the Smagorinsky coefficient has been measured as a function of the mean shear and stability condition of the atmosphere as determined from the average surface heat and momentum fluxes. However, in LES the global average field values are often difficult to determine a priori and the SGS parameters ideally must be expressed as a function of local flow variables that characterize the instantaneous flow phenomena. With the goal of improving the Smagorinsky closure, in this study several dimensionless parameters characterizing the local structure and important dynamical characteristics of the flow are defined. These local parameters include enstrophy, vortex stretching, self-amplification of strain rate, and normalized temperature gradient and all are defined in such a way that they remain bounded under all circumstances. The dependence of the Smagorinsky coefficient on these local parameters is studied a priori from field data measured in the atmospheric surface layer and, as a reference point, from direct numerical simulation of neutrally buoyant, isotropic turbulence. To capture the local effects in a statistically meaningful fashion, conditional averaging is used. Results show various important and interrelated trends, such as significant increases of the coefficient in regions of large strain-rate self-amplification and vortex stretching. Results also show that the joint dependence on the parameters is rather complicated and cannot be described by products of functions that depend on single parameters. Dependence on locally defined parameters is expected to improve the SGS model by sensitizing it to local flow conditions and by enabling possible generalizations of the dynamic model based on conditional averaging.

Corresponding author address: Charles Meneveau, Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218. Email: meneveau@jhu.edu

Abstract

Phenomena such as large-scale shear, buoyancy, and the proximity to the ground surface significantly affect interactions among scales in atmospheric boundary layer turbulent flows. Hence, these phenomena impact parameters that enter subgrid-scale (SGS) parameterizations used in large eddy simulations (LES) of the atmospheric boundary layer. The effects of these phenomena upon SGS parameters have, to date, been studied mostly as functions of the global state of the flow. For instance, the Smagorinsky coefficient has been measured as a function of the mean shear and stability condition of the atmosphere as determined from the average surface heat and momentum fluxes. However, in LES the global average field values are often difficult to determine a priori and the SGS parameters ideally must be expressed as a function of local flow variables that characterize the instantaneous flow phenomena. With the goal of improving the Smagorinsky closure, in this study several dimensionless parameters characterizing the local structure and important dynamical characteristics of the flow are defined. These local parameters include enstrophy, vortex stretching, self-amplification of strain rate, and normalized temperature gradient and all are defined in such a way that they remain bounded under all circumstances. The dependence of the Smagorinsky coefficient on these local parameters is studied a priori from field data measured in the atmospheric surface layer and, as a reference point, from direct numerical simulation of neutrally buoyant, isotropic turbulence. To capture the local effects in a statistically meaningful fashion, conditional averaging is used. Results show various important and interrelated trends, such as significant increases of the coefficient in regions of large strain-rate self-amplification and vortex stretching. Results also show that the joint dependence on the parameters is rather complicated and cannot be described by products of functions that depend on single parameters. Dependence on locally defined parameters is expected to improve the SGS model by sensitizing it to local flow conditions and by enabling possible generalizations of the dynamic model based on conditional averaging.

Corresponding author address: Charles Meneveau, Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218. Email: meneveau@jhu.edu

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