Summary
A variational principle for fluid mechanics is derived without calling for any additional postulates in any ad hoc way. In the principle derived here, the Lagrangian is essentially the sum of kinetic and heat energy transferred to the fluid, less the sum of its internal and potential energy, less the work done on its exterior (similar to the enthalpy concept), rather than the difference between only kinetic energy and internal energy, as obtained previously by Seliger and Whitham [1] for a more restricted mode of variation.
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References
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Tran-Cong, T. A variational principle for fluid mechanics. Arch. Appl. Mech. 67, 96–104 (1996). https://doi.org/10.1007/BF00787143
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DOI: https://doi.org/10.1007/BF00787143