A higher order acoustic equation for the slightly viscous case

摘要

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 S = M-n, the equation obtained is correct to order M-n. M is the Mach number (the speed of the fluid divided by the local speed of sound). S is the Stokes number, (the kinematic viscosity divided by the product of the wavelength and the local speed of sound). For n = 1, the equation reduces to the Kuznetsov equation. [References: 10]