A discontinuous variational principle implying a non-equilibrium dispersion relation for damped acoustic waves. (English) Zbl 1462.76165
Summary: The discontinuous Lagrangian approach, allowing for a variational description of irreversible phenomena in continuum theory such as viscosity and thermal conductivity, is utilised for the analysis of damped acoustic waves. Starting from a Lagrangian for general viscous flow theory, by linearisation of the resulting Euler-Lagrange equations and performing an ensemble average, a single wave equation for the density perturbations is obtained, being the one resulting from classical Navier-Stokes theory with an additional term due to thermodynamic non-equilibrium. By considering harmonic waves, the respective non-classical dispersion relation and its implications are analysed.
MSC:
| 76Q05 | Hydro- and aero-acoustics |
| 76M30 | Variational methods applied to problems in fluid mechanics |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
Keywords:
discontinuous Lagrangian approach; viscosity; thermal conductivity; thermal excitation fieldReferences:
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