A Higher Order Acoustic Equation for the Slightly Viscous Case

Authors: Söderholm,  L. H. S.
Document Type: Article
Pubstate: Published
Journal: Acta Acustica
Volume: 87   29-33
Year: 2001


Compressible flow of a Newtonian fluid is studied in the fully nonlinear approximation and to lowest order in the dissipation. Nonlinear contributions to dissipation are neglected. It is shown that entropy can then be eliminated. An initially vorticity free flow is shown to remain vorticity free. An acoustic equation is derived. If $K=Ma^$, the equation obtained is correct to order $Ma^$. $K$ is the dimensionless number characterizing the size of the dissipative corrections to the wave equation. In the case of a gas, $K$ is the Knudsen number. For $n=1$, the equation reduces to the Kuznetsov equation.