In the context of water waves, we consider a resonator with deep subwavelength resonance, analogue to the Helmholtz resonator in acoustics. In the shallow water regime, using asymptotic analysis, a one-dimensional model is derived in which the effect of the resonator is reduced to effective transmission conditions. These conditions clearly highlight two contributions. The first is associated with the dock on its own and it is responsible for a jump of the potential at the free surface. The second is due to the resonant cavity and it is responsible for a jump in the horizontal velocity. It involves as well the uniform amplitude within the resonant cavity with a transient dynamics explicitly given by the equation of a damped oscillator forced by the incident waves. The one-dimensional model is validated in the harmonic regime by comparison to direct two-dimensional numerics. It is shown to reproduce accurately the scattering coefficients and the amplitude within the resonator; interestingly, this remains broadly true for finite water depths. We further inspect the spatio-temporal behaviour of different types of wave packets interacting with the resonating and radiating cavity.

The control of guided water wave propagation based on the Autler-Townes splitting resonance concept is demonstrated experimentally, numerically, and theoretically. Complete wave absorption is achieved using an asymmetric pointlike scatterer made of two closely spaced resonant side channels connected to a guide and designed so that its energy leakage is in perfect balance with the inherent viscous losses in the system. We demonstrate that the nature of the resonators and guide junction completely controls the positions of the wave numbers at the reflection and transmission zeros on the real axis; the asymmetry of the resonators completely controls their positions on the imaginary axis. Thus, by adjusting these two independent parameters, we obtain a zero reflection and transmission.

We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch–Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem.

We present a theoretical and experimental study of a resonator of the Helmholtz type for the control of the swell. An experimental demonstration of the shielding effect by a belt made of evenly distributed resonators is given. We then provide in-depth analysis of the Fano resonance resulting from the interference between the dock scattering (the background) and the resonant cavity scattering. This is done thanks to space–time resolved experiments which provides the complex-valued scattering coefficients and amplitude within the resonator. We provide a one-dimensional model derived in the shallow water regime owing to asymptotic analysis. The model contains the two ingredients of the Fano resonance and allows us to exhibit the damping due to leakage. When adding heuristically the damping due to losses, it reproduces the main features of the resonance observed experimentally.

This study investigates the potential use of an active device to efficiently absorb water waves propagating in a channel. The active device comprises a dipole source consisting of two sources in quasi-opposition of phase. We explore the feasibility of this approach to achieve perfect absorption of guided waves through interference phenomena. To accomplish this, we establish the law governing the waves emitted by the dipole source to optimize the absorption of specific incident waves. The validity of this law is demonstrated through numerical simulations and laboratory experiments, encompassing both the harmonic and transient regimes of the experimental set-up.