Soft Matter and Complex Systems Seminar

Controlling surface water wave propagation is crucial for wave manipulation and cloaking technologies. By leveraging the invariance of shallow water equations under coordinate transformations, objects can be rendered invisible to incident waves. Traditional transformations often require spatially anisotropic bathymetries, which typically violate the assumptions of the depth-averaged models describing the propagation of water waves. We demonstrate that conformal mapping, which provides smoothly varying bathymetry, can be effectively applied to water waveguide systems with defects in the form of local variations in the waveguide wall shape. Our approach successfully cloaks these defects across a broad range of frequencies, including regimes where dispersive effects are significant. Despite the inherent dispersive nature of water waves, forward scattering remains weak, ensuring robust cloaking performance. Experimental results validate the broadband capabilities of this method.

Based on the results obtained in the case of the meandering waveguide, we present a novel technique to render objects invisible to incident waves in a water waveguide system with parallel walls at low frequencies. The invisibility of a waveguide defect, specifically a vertical surface-piercing circular cylinder, is achieved through local deformations of the waveguide walls in the immediate vicinity of the defect. Our method results in a reflection coefficient that is at least 20 times lower than in the case of a parallel waveguide. The effect is observed over a broad frequency range. Experimental results confirm the high efficiency of our approach, showing that backscattered energy is reduced by a factor of 100 to 5000 compared to the reference case within the considered frequency range.