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Use of the Gibbs thermodynamic potential to express the equation of state in atmospheric models
Author(s) -
Thuburn J.
Publication year - 2017
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3020
Subject(s) - spurious relationship , compressibility , gibbs free energy , gibbs–helmholtz equation , thermodynamic state , thermodynamic equations , equation of state , statistical physics , thermodynamic process , entropy (arrow of time) , mathematics , thermodynamics , physics , non equilibrium thermodynamics , material properties , statistics
The thermodynamics of moist processes is complicated, and in typical atmospheric models numerous approximations are made. However, they are not always made in a self‐consistent way, which could lead to spurious sources or sinks of energy and entropy. One way to ensure self‐consistency is to derive all thermodynamic quantities from a thermodynamic potential such as the Gibbs function. Approximations may be made to the Gibbs function; these approximations are inherited by all derived quantities in a way that guarantees self‐consistency. Here, the feasibility of using the Gibbs function in an atmospheric model is demonstrated through the development of a semi‐implicit, semi‐Lagrangian vertical slice model, and its application to a standard buoyant bubble test case. The flexibility of the approach is also demonstrated by running the test case with four different equations of state corresponding to dry air, moist air that is saturated, a pseudo‐incompressible fluid, and an incompressible fluid. A recently presented ‘blended’ equation set that unifies the dry fully compressible case and the pseudo‐incompressible case is also easily accommodated.