On the Kuznetsov equation and higher order nonlinear acoustics equations

Compressible flow of a Newtonian fluid is studied in the fully nonlinear approximation and to lowest order in the dissipation, neglecting cross terms Ma . Kn (Ma is the Mach number, Kn the Knudsen number). An initially vorticity free flow is shown to remain vorticity free. An acoustic equation is derived. If Kn = Ma(n), the equation obtained is correct to order Ma(n). For n = 1, it reduces to the Kuznetsov equation.