Small water channel network for designing wave fields in shallow water

Abstract

A small water channel network is proposed for designing shallow water fields, and the network is applied to attain water wave cloaking. The design formula is derived from an analogy between waves in a water channel and in an electric circuit; an approach of a transmission line metamaterial is extended to water waves and the water channel is used as an alternative of the transmission line. The size of the water channel is sufficiently smaller than the wavelength and a number of the channels are periodically connected as a network. This small water channel network makes artificial wave fields, and it works for a wide band of frequencies. First, we make an isotropic network equivalent to a shallow water space with constant depth in order to validate the proposed design method. It shows no wave reflection at the interface due to impedance matching. After that, the proposed theory is applied to designing an anisotropic small water channel network for demonstrating shallow water cloaking. A cylinder is cloaked from waves by the network surrounding the cylinder. Both cases are confirmed with numerical computations by solving the boundary-value problem based on linear potential theory.

Water wave cloaking using a floating composite plate

“…The use of nonlinear transformation of a cylindrical region can keep the gravitational acceleration at a constant value, and only change in the sea bed topography is used to achieve cloaking from shallow-water waves (Zareei & Alam 2015). Alternative approaches are to use an array of bottom-mounted objects for implementing a cloaking device for shallow-water surface gravity waves using the coordinate transformation technique (Dupont et al 2016;Iida & Kashiwagi 2018) or capillary-gravity waves (Farhat et al 2008).…”

“…Alternative approaches are to use an array of bottom-mounted objects for implementing a cloaking device for shallow-water surface gravity waves using the coordinate transformation technique (Dupont et al. 2016; Iida & Kashiwagi 2018) or capillary-gravity waves (Farhat et al. 2008).…”

Time domain modelling of a Helmholtz resonator analogue for water waves

“…Maurel et al (2017), Maurel, Pham & Marigo (2019) and Porter (2019), or it can be guided due to valley-locked transport (Makwana et al 2020). In addition, a plethora of interesting phenomena has been proposed, such as the cancellation of the scattering by rigid obstacles and their cloaking (Newman 2014;Dupont et al 2016;Porter 2018;Bobinski et al 2018;Iida & Kashiwagi 2018;Farhat et al 2020), the perfect absorption of the wave energy in the nonlinear regime (Monsalve et al 2019) and the trapping for energy harvesting using graded arrays of resonators (Bennetts, Peter & Craster 2018, 2019.…”

Control of the Swell by an Array of Helmholtz Resonators

“…For instance, the propagation can be made anisotropic using varying bathymetry see e.g., [3][4][5], or it can be guided due to valley-locked transport [6]. In addition, a plethora of interesting phenomena has been proposed, such as the cancellation of the scattering by rigid obstacles and their cloaking [7][8][9][10][11][12], the perfect absorption of the wave energy in the nonlinear regime [13] and the trapping for energy harvesting using graded arrays of resonators [14,15].…”