Recent research on wave propagation and scattering in materials with spatiotemporal modulation (STM) of bulk properties or boundary conditions has gained interest in order to improve control of wave energy in both time and space. This work employs coupled mode theory (CMT) that was derived to study acoustic waves incident from a half-space and reflected from a fluid waveguide that has a STM boundary impedance. CMT for this system shows that coupling between propagating and evanescent modes exists at frequency–wavenumber combinations related to the modulation frequency and wavenumber that cannot be achieved without boundary modulation. We investigate the case of waveguide excitation by evanescent fields on the non-modulated boundary between a fluid waveguide and a fluid half-space while the opposite boundary is assumed to be an elastic plate with STM stiffness. The “incident” evanescent wave mimics the case of acoustic forcing from turbulent flow, which can generate waves that propagate within the waveguide and plate. We show that STM of the plate stiffness can be used to couple incident evanescent energy into modes at different frequencies and wavenumbers, which can be used to further control the generated waves from turbulence such as nonreciprocal redirection and absorption of the acoustic energy.
Goldsberry et al. (Wed,) studied this question.