A Spectral Parameterization of Drag, Eddy Diffusion, and Wave Heating for a Three-Dimensional Flow Induced by Breaking Gravity Waves

Xun Zhu Applied Physics Laboratory, The Johns Hopkins University, Baltimore, Maryland

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Jeng-Hwa Yee Applied Physics Laboratory, The Johns Hopkins University, Baltimore, Maryland

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William H. Swartz Applied Physics Laboratory, The Johns Hopkins University, Baltimore, Maryland

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Elsayed R. Talaat Applied Physics Laboratory, The Johns Hopkins University, Baltimore, Maryland

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Lawrence Coy U.S. Naval Research Laboratory, Washington, D.C

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Abstract

There are three distinct processes by which upward-propagating gravity waves influence the large-scale dynamics and energetics of the middle atmosphere: (i) nonlocalized transport of momentum through wave propagation in three dimensions that remotely redistributes atmospheric momentum in both zonal and meridional directions from wave generation to wave dissipation regions; (ii) localized diffusive transport of momentum, heat, and tracers due to mixing induced by wave breaking; and (iii) localized transport of heat by perturbing wave structures due to dissipation that redistributes the thermal energy within a finite domain. These effects become most significant for breaking waves when momentum drag, eddy diffusion, and wave heating— the “breaking trinity”—are all imposed on the background state. This paper develops a 3D parameterization scheme that self-consistently includes the breaking trinity in large-scale numerical models. The 3D parameterization scheme is developed based on the general relationship between the wave action flux and the subgrid-scale momentum and heat fluxes developed by Zhu in 1987 and a mapping approximation between the wave source spectrum and momentum deposition distribution developed by Alexander and Dunkerton in 1999. For a set of given input wind and temperature profiles at each model grid, the parameterization scheme outputs the vertical profiles of the subgrid-scale force terms together with the eddy diffusion coefficients in the momentum and energy equations for a 3D background flow.

Corresponding author address: Dr. Xun Zhu, The Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723–6099. Email: xun.zhu@jhuapl.edu

A comment reply has been published regarding this article and can be found at http://journals.ametsoc.org/doi/full/10.1175/2011JAS3663.1 and http://journals.ametsoc.org/doi/full/10.1175/2011JAS3738.1

Abstract

There are three distinct processes by which upward-propagating gravity waves influence the large-scale dynamics and energetics of the middle atmosphere: (i) nonlocalized transport of momentum through wave propagation in three dimensions that remotely redistributes atmospheric momentum in both zonal and meridional directions from wave generation to wave dissipation regions; (ii) localized diffusive transport of momentum, heat, and tracers due to mixing induced by wave breaking; and (iii) localized transport of heat by perturbing wave structures due to dissipation that redistributes the thermal energy within a finite domain. These effects become most significant for breaking waves when momentum drag, eddy diffusion, and wave heating— the “breaking trinity”—are all imposed on the background state. This paper develops a 3D parameterization scheme that self-consistently includes the breaking trinity in large-scale numerical models. The 3D parameterization scheme is developed based on the general relationship between the wave action flux and the subgrid-scale momentum and heat fluxes developed by Zhu in 1987 and a mapping approximation between the wave source spectrum and momentum deposition distribution developed by Alexander and Dunkerton in 1999. For a set of given input wind and temperature profiles at each model grid, the parameterization scheme outputs the vertical profiles of the subgrid-scale force terms together with the eddy diffusion coefficients in the momentum and energy equations for a 3D background flow.

Corresponding author address: Dr. Xun Zhu, The Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723–6099. Email: xun.zhu@jhuapl.edu

A comment reply has been published regarding this article and can be found at http://journals.ametsoc.org/doi/full/10.1175/2011JAS3663.1 and http://journals.ametsoc.org/doi/full/10.1175/2011JAS3738.1

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