On the Application of the Dynamic Smagorinsky Model to Large-Eddy Simulations of the Cloud-Topped Atmospheric Boundary Layer

M. P. Kirkpatrick Center for Turbulence Research, Stanford University, Stanford, California

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A. S. Ackerman NASA Ames Research Center, Moffett Field, California

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D. E. Stevens Lawrence Livermore National Laboratory, Livermore, California

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N. N. Mansour Center for Turbulence Research, Stanford University, Stanford, California

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Abstract

In this paper the dynamic Smagorinsky model originally developed for engineering flows is adapted for simulations of the cloud-topped atmospheric boundary layer in which an anelastic form of the governing equations is used. The adapted model accounts for local buoyancy sources, vertical density stratification, and poor resolution close to the surface and calculates additional model coefficients for the subgrid-scale fluxes of potential temperature and total water mixing ratio. Results obtained with the dynamic model are compared with those obtained using two nondynamic models for simulations of a nocturnal marine stratocumulus cloud deck observed during the first research flight of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field experiment. The dynamic Smagorinsky model is found to give better agreement with the observations for all parameters and statistics. The dynamic model also gives improved spatial convergence and resolution independence over the nondynamic models. The good results obtained with the dynamic model appear to be due primarily to the fact that it calculates minimal subgrid-scale fluxes at the inversion. Based on other results in the literature, it is suggested that entrainment in the DYCOMS-II case is due predominantly to isolated mixing events associated with overturning internal waves. While the behavior of the dynamic model is consistent with this entrainment mechanism, a similar tendency to switch off subgrid-scale fluxes at an interface is also observed in a case in which gradient transport by small-scale eddies has been found to be important. This indicates that there may be problems associated with the application of the dynamic model close to flow interfaces. One issue here involves the plane-averaging procedure used to stabilize the model, which is not justified when the averaging plane intersects a deforming interface. More fundamental, however, is that the behavior may be due to insufficient resolution in this region of the flow. The implications of this are discussed with reference to both dynamic and nondynamic subgrid-scale models, and a new approach to turbulence modeling for large-eddy simulations is proposed.

* Current affiliation: School of Engineering, University of Tasmania, Tasmania, Australia

Corresponding author address: Michael Kirkpatrick, School of Engineering, Private Bag 65, University of Tasmania, Hobart, Tasmania 7001, Australia. Email: michael.kirkpatrick@utas.edu.au

Abstract

In this paper the dynamic Smagorinsky model originally developed for engineering flows is adapted for simulations of the cloud-topped atmospheric boundary layer in which an anelastic form of the governing equations is used. The adapted model accounts for local buoyancy sources, vertical density stratification, and poor resolution close to the surface and calculates additional model coefficients for the subgrid-scale fluxes of potential temperature and total water mixing ratio. Results obtained with the dynamic model are compared with those obtained using two nondynamic models for simulations of a nocturnal marine stratocumulus cloud deck observed during the first research flight of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field experiment. The dynamic Smagorinsky model is found to give better agreement with the observations for all parameters and statistics. The dynamic model also gives improved spatial convergence and resolution independence over the nondynamic models. The good results obtained with the dynamic model appear to be due primarily to the fact that it calculates minimal subgrid-scale fluxes at the inversion. Based on other results in the literature, it is suggested that entrainment in the DYCOMS-II case is due predominantly to isolated mixing events associated with overturning internal waves. While the behavior of the dynamic model is consistent with this entrainment mechanism, a similar tendency to switch off subgrid-scale fluxes at an interface is also observed in a case in which gradient transport by small-scale eddies has been found to be important. This indicates that there may be problems associated with the application of the dynamic model close to flow interfaces. One issue here involves the plane-averaging procedure used to stabilize the model, which is not justified when the averaging plane intersects a deforming interface. More fundamental, however, is that the behavior may be due to insufficient resolution in this region of the flow. The implications of this are discussed with reference to both dynamic and nondynamic subgrid-scale models, and a new approach to turbulence modeling for large-eddy simulations is proposed.

* Current affiliation: School of Engineering, University of Tasmania, Tasmania, Australia

Corresponding author address: Michael Kirkpatrick, School of Engineering, Private Bag 65, University of Tasmania, Hobart, Tasmania 7001, Australia. Email: michael.kirkpatrick@utas.edu.au

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