Weakly nonlinear waves and acoustic streaming produced by a vibrating strip flush with a plane wall

Abstract

The weakly nonlinear propagation of a two‐dimensional wave, which is radiated into a half‐space from a sinusoidally vibrating strip mounted on a plane wall, is studied theoretically. It is supposed that the wavelength of radiated waves is of the same order as the width of the strip, and that the acoustic Reynolds number is sufficiently large. The entire propagation process, from generation of sound to the stage where the amplitude of a sawtooth wave is saturated, is analyzed in the leading‐order approximation. In a near field, linear wave theory is valid to first approximation. The asymptotic form of its time‐averaged acoustic intensity can have sidelobes in addition to a central lobe. Acoustic streaming occurs near the strip in the next order, whose flow pattern differs according to a normalized frequency which is less or greater than a critical frequency. In the far field, a simple‐wave equation is exactly solved and the subsequent evolution into the sawtooth wave is examined using the equal‐areas rule. These two‐dimensional waves may be regarded as cylindrical waves with directivity. At greater distances, the amplitude saturation becomes independent of direction.