The connection between the principle of the least action and the thermodynamic condition of stability

: The direct correlation between classical mechanics of material points (Lagrange principle of classical mechanics) and classical continuum mechanics can be established when the existence of a trajectory and a friction force are added. The important role of the total enthalpy follows from a variational analysis. More-over, the thermodynamic criterion of the stability is formulated using the total enthalpy and compared with the experiments, numerical and the classical Rayleigh theory supports its applicability. It was shown that the solid body vortex is at the margin of stability, which is experimentally observed. Analogously, the potential vortex is by the thermodynamic criterion stable, however by the Rayleigh criteria it is on the onset of stability. The loss of stability of the forsed vortex (solid body vortex) is the main reason why it transforms into a free vortex (potential vortex). The classical Taylor experiment of flow between two rotating cylinders is analyzed from the point of view of this criterion. Recently, the vortex transformation process has been demonstrated both experimentally and by numerical simulations for the case of a vortex tube at the Institute of Aerospace Thermodynamics at Stuttgart (Seibold, 2022) and experimentally for the annular nozzle flow at the Institute of Thermomechanics CAS in Prague.