A mathematical study of water wave interaction with a thin perforated barrier in a two-layer fluid over a permeable bottom

This article studies the impact of a submerged interface-piercing perforated barrier in a two-layer fluid flowing over a permeable bottom. We investigate oblique wave scattering, trapping and radiation due to the structure focusing on the bottom permeability. The dead water phenomenon is analysed with the consideration of the bottom permeability, which results in a higher variation of the interfacial wave due to the bottom permeability. The matched eigenfunction expansion method and the least square technique are used to calculate various hydrodynamic coefficients. Wave energy identity relation is derived for the scattering scenario, and the associated energy loss due to the barrier is calculated. In order to attain the maximum wave dissipation, an ideal porous-effect parameter of the barrier is proposed for consideration, and it is observed that larger values of porous-effect parameter result in the lowest feasible pressure distribution. A good comparison with a prior result justifies the current semi-analytical procedure. Furthermore, the verification of the energy-identity terms aid in the validation of the computed results. Additionally, wave trapping in a confined region is examined by investigating reflection coefficients by considering a rigid wall. The thin perforated barrier model is further considered for examining the radiation aspect while considering its slow motion. For various porous-effect parameters of the barrier, the amplitude ratio of the radiated potential is investigated, and it is clearly observed that higher frequency significantly lowers the amplitude for both free surface and interfacial propagating modes. The impact of the perforated barrier is analysed by investigating the essential hydrodynamic coefficients, namely, added mass and damping coefficient.