A Lagrangian for Compressible Flow Focusing on Dissipation due to Thermal Conduction

ABSTRACT With the aim of describing compressible viscous flows by means of a variational principle that takes into account heat conduction, a recently proposed Lagrangian is subjected to a detailed linear wave analysis that stems directly from the Lagrangian. The accompanying thermodynamic equation of state employed leads to a natural decomposition of the conduction term into three contributions, with the importance of each accessed through a detailed analysis employing a recently developed perturbation methodology giving rise to a favorable system of governing Jacobi equations. In addition to the model Lagrangian itself, three potential model scenarios—based on different combinations of the contributions forming the Lagrangian—are rigorously evaluated and appraised, regarding the occurrence, or otherwise, of dissipation recognizable by an attenuation of harmonic waves. Results reveal that two of the four models are suitable candidates, and suggest one in particular.