具有热力学非平衡效应的阻尼声波的弱非线性波方程
A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects
摘要：
传播的非线性声波的问题被认为是解决方案，其中，无论是有阻尼和无阻尼，已获得迄今为止从Navier-Stokes-Duhem方程连同连续性和热传导方程。这里报道的新方法采用的是一种不连续拉格朗日方法，即从Hamilton原理中得到的一般粘性流的不连续拉格朗日方法。结果表明，系综平均的运动方程产生的欧拉-拉格朗日方程，无旋流动的假设下，导致一个弱非线性波方程的速度势：实际上是一个概括的库兹涅佐夫的众所周知的方程，由于热力学非平衡效应的额外条款。
英文摘要：
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.
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