The current formulation of dry convection in AGNI uses a lapse rate (DALR) equivalent to R/(mu*c_p), which has been adapted to suit the non-ideal hydrostatic height integrator. However, this still does not account for the compressibility of the gas mixture within convective regions, nor check for enthalpy conservation.
This makes the DALR calculation semi-ideal, but not a completely non-ideal formulation. It should be possible to express the DALR (dT/dP at constant entropy) from thermodynamic principles if we can obtain the internal energy of each component. This is tabulated by AQUA and by CMS19. For ideal+VdW gases it is analytic, but could easily be tabulated.
PseudoAdiabaticProcesses-dtarb.pdf
https://www.thermal-engineering.org/what-is-internal-energy-of-an-ideal-gas-definition/
https://physics.stackexchange.com/a/47097
https://cornerstone.lib.mnsu.edu/cgi/viewcontent.cgi?article=1062&context=avia-fac-pubs
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/The_Live_Textbook_of_Physical_Chemistry_(Peverati)/11%3A_Ideal_and_Non-Ideal_Gases/11.02%3A_Behaviors_of_Non-Ideal_Gases
http://personal.rhul.ac.uk/UHAP/027/PH4211/PH4211_files/Chapter3--.pdf
Some previous work has assessed non-ideal DALR calculations, but only in the case of the VdW EOS.
ArXiv post - 2007.13896v2.pdf
It should be noted that the DALR provided by the AQUA EOS table apparently contains incorrect values. The DALR for water should therefore be computed using the internal energy in the tables.
Furthermore, the velocity calculation in the MLT formulation is based on the mixing length ($\lambda$) and the Brunt-Vaisala frequency ($N$). The current formulation expresses $N$ as if the atmosphere were an ideal gas, but we should calculate this more generally.
https://en.wikipedia.org/wiki/Brunt%E2%80%93V%C3%A4is%C3%A4l%C3%A4_frequency?useskin=vector
And more recently:
https://arxiv.org/abs/2508.05578
The current formulation of dry convection in AGNI uses a lapse rate (DALR) equivalent to R/(mu*c_p), which has been adapted to suit the non-ideal hydrostatic height integrator. However, this still does not account for the compressibility of the gas mixture within convective regions, nor check for enthalpy conservation.
This makes the DALR calculation semi-ideal, but not a completely non-ideal formulation. It should be possible to express the DALR (dT/dP at constant entropy) from thermodynamic principles if we can obtain the internal energy of each component. This is tabulated by AQUA and by CMS19. For ideal+VdW gases it is analytic, but could easily be tabulated.
PseudoAdiabaticProcesses-dtarb.pdf
https://www.thermal-engineering.org/what-is-internal-energy-of-an-ideal-gas-definition/
https://physics.stackexchange.com/a/47097
https://cornerstone.lib.mnsu.edu/cgi/viewcontent.cgi?article=1062&context=avia-fac-pubs
https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/The_Live_Textbook_of_Physical_Chemistry_(Peverati)/11%3A_Ideal_and_Non-Ideal_Gases/11.02%3A_Behaviors_of_Non-Ideal_Gases
http://personal.rhul.ac.uk/UHAP/027/PH4211/PH4211_files/Chapter3--.pdf
Some previous work has assessed non-ideal DALR calculations, but only in the case of the VdW EOS.
ArXiv post - 2007.13896v2.pdf
It should be noted that the DALR provided by the AQUA EOS table apparently contains incorrect values. The DALR for water should therefore be computed using the internal energy in the tables.
Furthermore, the velocity calculation in the MLT formulation is based on the mixing length ($\lambda$ ) and the Brunt-Vaisala frequency ($N$ ). The current formulation expresses $N$ as if the atmosphere were an ideal gas, but we should calculate this more generally.
https://en.wikipedia.org/wiki/Brunt%E2%80%93V%C3%A4is%C3%A4l%C3%A4_frequency?useskin=vector
And more recently:
https://arxiv.org/abs/2508.05578