A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models
Shaw, T. A. and Shepherd, T. G. (2009) A theoretical framework for energy and momentum consistency in subgrid-scale parameterization for climate models. Journal of the Atmospheric Sciences, 66. pp. 3095-3114. ISSN 1520-0469
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To link to this article DOI: 10.1175/2009JAS3051.1
A theoretical framework for the joint conservation of energy and momentum in the parameterization of subgrid-scale processes in climate models is presented. The framework couples a hydrostatic resolved (planetary scale) flow to a nonhydrostatic subgrid-scale (mesoscale) flow. The temporal and horizontal spatial scale separation between the planetary scale and mesoscale is imposed using multiple-scale asymptotics. Energy and momentum are exchanged through subgrid-scale flux convergences of heat, pressure, and momentum. The generation and dissipation of subgrid-scale energy and momentum is understood using wave-activity conservation laws that are derived by exploiting the (mesoscale) temporal and horizontal spatial homogeneities in the planetary-scale flow. The relations between these conservation laws and the planetary-scale dynamics represent generalized nonacceleration theorems. A derived relationship between the wave-activity fluxes-which represents a generalization of the second Eliassen-Palm theorem-is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.