A weakly nonlinear wave equation for damped acoustic waves with\n thermodynamic non-equilibrium effects

2020/12/28 by M. Scholle, Scholle, Markus
Earth and Planetary Sciences · Engineering · #76A02 #76Q05 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Pattern Formation and Solitons (nlin.PS) #Seismic Waves and Analysis #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2012.14399

openalex publication_date 2020/12/28 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

The problem of propagating nonlinear acoustic waves is considered; the\nsolution to which, both with and without damping, having been obtained to-date\nstarting from the Navier-Stokes-Duhem equations together with the continuity\nand thermal conduction equation. The novel approach reported here adopts\ninstead, a discontinuous Lagrangian approach, i.e. from Hamilton's principle\ntogether with a discontinuous Lagrangian for the case of a general viscous\nflow. It is shown that ensemble averaging of the equation of motion resulting\nfrom the Euler-Lagrange equations, under the assumption of irrotational flow,\nleads to a weakly nonlinear wave equation for the velocity potential: in effect\na generalisation of Kuznetsov's well known equation with an additional term due\nto thermodynamic non-equilibrium effects.\n

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