Wave Scattering by Small Undulation on the Porous Bottom of an Ocean in the Presence of Surface Tension

Abstract

The scattering of incident surface water waves due to small bottom undulation on the porous bed of a laterally unbounded ocean in the presence of surface tension at the free surface is investigated within the framework of two-dimensional linearized water wave theory. Perturbation analysis in conjunction with the Fourier transform technique is employed to derive the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. One special type of bottom topography is considered as an example and the related coefficients are determined in detail. These coefficients are presented in graphical forms. The theoretical observations are validated computationally. The results for the problem involving scattering of water waves by bottom deformations on an impermeable ocean bed are obtained as a particular case.

Water-Waves Scattering by Permeable Bottom in Two-Layer Fluid in the Presence of Surface Tension

“…Chakrabarti and Sahoo [7] studied the effect of surface tension in a single layer fluid using mixed-type Fourier transform in the case of infinite depth and the method of eigenfunction expansion in the case of finite depth. Using Fourier transform technique, Panda et al [25] studied the scattering of water waves in a single layer fluid over a permeable bottom by considering the effect of surface tension. Harter et al [1] analyzed the effect of surface tension on trapped modes.…”

Wave blocking and Bragg resonance in two-layer fluid with current and surface tension.

“…To investigate the influence of surface tension on progressive waves caused by vertical wave producers, Rhodes-Robinson [29] devised an effective reduction approach. Panda et al [25] investigated the scattering of water waves in a single layer fluid across a permeable bottom using the Fourier transform approach, taking into account the influence of surface tension. The inclusion of surface tension modifies the streamline pattern's qualitative characteristics, therefore they noted that it is not always justified to exclude it out of the problem formulation.…”