The effects of circumferential location-defects on the cloaking phenomenon for water waves are investigated. The cloaking condition means the absence of scattered waves radiating to infinity; that is, the cloaked structure appears invisible to a far-field observer. To accurately study this type of wave-structure-interaction problem, the higher-order boundary element method combined with wave interaction theory is adopted. Both the scattered wave energy and the wave drift forces are calculated and analyzed for the different defect cases of cylinders.
The cloaking phenomenon, originally proposed for electromagnetic waves (Pendry et al., 2006), is an effective method to protect the structure in waves. Here, cloak means no scattered waves radiate to infinity and the vertical cylinder appears invisible to the far-field observer. For water waves, the scattering cancellation method is a typical way to cloak a structure in waves.
Porter (2011) firstly proposed cloaking a vertical cylinder in shallow water by designing the topography in the region surrounding this cylinder, based on the scattering cancellation method. In order to obtain the proper topography, an optimization method was introduced to minimize the scattered wave energy of the vertical cylinder while the mild-slope equation was taken as the governing equation. Then, Newman (2012) confirmed the results obtained in Porter (2011) using a three-dimensional boundary element method. The reduction of the wave drift force on the vertical cylinder was found by Porter and Newman (2014); this puts forward a practical application of the cloaking phenomenon in ocean engineering.
However, the method associated with changing topography is effective only for shallow water. To cloak a structure in deep water, Newman (2013, 2014) proposed attaching surrounding truncated cylinders or a continuous ring. It was validated that the scattered wave energy and wave drift force of the structures can be significantly reduced to almost zero with the cloaking configuration. Following Newman’s works, Iida et al. (2014, 2015) numerically and experimentally confirmed the reduction of wave drift force by cloaking phenomenon. It was found that the wave drift force acting not only on the whole structure but also on the inner cylinder can be significantly reduced to almost zero. Read et al. (2016) performed further experimental research of the cloaking phenomenon for a circular cylinder surrounded by a circumferential array of eight cylinders to investigate the potential interferences that may affect the measurements. Zhang et al. (2017) demonstrated a periodic quasicloaking phenomenon with varying distances between the inner and the outer cylinders. Subsequently, Zhang et al. (2019a) experimentally and numerically investigated the wave elevation in the vicinity of the inner cylinder and the wave drift force on the inner cylinder under a series of different wave directions. It was found that the wave drift forces acting on the inner cylinder are closely related to the corresponding wave pattern.