The spatial scattering of sound by a mixing layer: Case of short waves

A high-order-accurate numerical model for the modified linearized Euler equations is employed to investigate the sound scattering of a plane wave by a temporally evolving mixing layer. The model is validated against benchmark cases to ensure its accuracy. Numerical results show that, as the convective Mach number increases and the characteristic scale ratio (defined as the ratio of the incident acoustic wavelength to the mixing layer's characteristic length) decreases, the acoustic scattering behavior transitions sequentially through the resonance regime and the geometrical-acoustics regime. Correspondingly, the scattered fields exhibit higher intensity, diminished symmetry, and greater irregularity. The study further reveals that the scattering generated by a mixing layer shares key similarities with that produced by a compact vortex, particularly in terms of scaling effects observed in the resonance regime, a characteristic not found in non-compact vortices. This similarity arises because the large-scale vortical structures in the mixing layer more closely resemble a compact vortex than a non-compact one. In the resonance regime, these structures act as compact acoustic sources, generating scattered waves with relatively symmetric directivity. In contrast, within the geometrical-acoustics regime, scattering is primarily governed by refraction and distortion effects resulting from the spatially varying flow field.