A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects
The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier–Stokes–Duhem equations together with the continuity and thermal conduction equation. The novel approach reported here adopts...
Gespeichert in:
Veröffentlicht in: | Wave motion 2022-02, Vol.109, p.102876, Article 102876 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier–Stokes–Duhem equations together with the continuity and thermal conduction equation. The novel approach reported here adopts instead, a discontinuous Lagrangian approach, i.e. from Hamilton’s principle together with a discontinuous Lagrangian for the case of a general viscous flow. It is shown that ensemble averaging of the equation of motion resulting from the Euler–Lagrange equations, under the assumption of irrotational flow, leads to a weakly nonlinear wave equation for the velocity potential: in effect a generalisation of Kuznetsov’s well known equation with an additional term due to thermodynamic non-equilibrium effects.
•Viscous flow with thermal conduction is deducible from a discontinuous Lagrangian.•Non-classical effects occur beyond thermodynamic equilibrium.•By ensemble averaging a non-classical equation of motion is derived.•In the irrotational and weakly nonlinear case a generalised Kuznetsov equation is obtained. |
---|---|
ISSN: | 0165-2125 1878-433X |
DOI: | 10.1016/j.wavemoti.2021.102876 |