Evolution of Rayleigh streaming flow velocity components in a resonant waveguide at high acoustic levels

The interaction between an acoustic wave and a solid wall generates a mean steady flow called Rayleigh streaming, generally assumed to be second order in a Mach number expansion. This flow is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at the antinode. For higher acoustic levels, additional streaming cells have been observed. In the present study, results of LDV and PIV measurements are compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming flows is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency upon acoustics going from quadratic to linear. The hypothesis of the radial streaming velocity being of second order in a Mach number expansion is shown to be invalid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components.