Thermodynamically consistent versions of approximations used in\n modelling moist air Article Swipe
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1002/qj.4353
· OA: W4289754999
Some existing approaches to modeling the thermodynamics of moist air make\napproximations that break $\\textit{thermodynamic consistency}$, such that the\nresulting thermodynamics do not obey the 1st and 2nd laws or have other\ninconsistencies. Recently, an approach to avoid such inconsistency has been\nsuggested: the use of $\\textit{thermodynamic potentials}$ in terms of their\n$\\textit{natural variables}$, from which all thermodynamic quantities and\nrelationships are derived. In this paper, we develop this approach for\n$\\textit{unapproximated}$ moist air thermodynamics and two widely used\napproximations: the constant $\\kappa$ approximation and the dry heat capacities\napproximation. The consistent constant $\\kappa$ approximation is particularly\nattractive because it leads to, when using virtual potential temperature\n$\\theta_v$ as the thermodynamic variable, adiabatic dynamics that depend only\non total mass, independent of the breakdown between water forms. Additionally,\na wide variety of material from different sources in the literature on\nthermodynamics in atmospheric modelling is brought together. It is hoped that\nthis paper provides a comprehensive reference for the use of thermodynamic\npotentials in atmospheric modelling, especially for the three systems\nconsidered here.\n