Nonlinear acoustical wave interactions in a rigid cylindrical waveguide with mean flow

In order to understand nonlinear wave propagation in applications such as exhaust pipes, jet engines, pipe flows, and blood flow in veins one can model them as nonlinear waveguides. There is a reasonable amount of numerical or analytical work in the literature on nonlinear rigid waveguides and much less on nonlinear flexible waveguides. However, most of these studies ignore the mean flow of the fluid. These waveguides under harmonic excitation, generate multiple harmonic waves and modes at frequencies dictated by the dispersion relation. Due to weak nonlinearity, these modes interact, leading to the formation of higher harmonics that either grow spatially or oscillate in amplitude. The current study examines nonlinear acoustic wave propagation in an infinite rigid cylindrical waveguide containing an acoustic fluid with uniform mean flow. The system is modelled using nonlinear acoustic equations, separated into first and second order components using the regular perturbation method. At first order, the dispersion equation determines the primary waves, revealing that an increase in Mach number reduces the primary wavenumber's magnitude. A closed form solution for pressure at both linear and nonlinear orders is derived, and wave interactions are explored. Resonance conditions and Mach number effects on the wave behaviour are investigated.