Small-amplitude sound waves in a viscous rotating compressible Newtonian fluid

For a rotating viscous compressible Newtonian fluid, the linearized Navier–Stokes equation, the continuity equation and the equation for isoentropic processes are simultaneously considered in order to obtain and equation for pressure waves. This equation is solved to get the dispersion law for such waves. In the dispersion law a non dimensional parameter $R$ in used, which is given by the relation between the characteristic damping time of the wave and the period of the fluid rotation. The limit of a viscous compressible static fluid is obtained. The numerical results of the dispersion relation are given for different values of the angle between the direction of the wave propagation and the rotation axis and for the values of $R$. The existence of gaps and of a typical waveguide effect are reported. The dispersion relation of the modes are given for the real and the imaginary parts of the wave vector.