Influences of a Varying Sill at the Seabed on Two-Dimensional Radiation of Linear Water Waves by a Rectangular Buoy

The presence of a sill alters the traditional flat seabed conditions, imposing significant effects on hydrodynamic characteristics of the wave–body interaction problem. Eigenfunction matching method (EMM), which is a typical analytical method, is employed to precisely evaluate these effects on two-dimensional radiation of linear water waves by a rectangular buoy. The agreement with the published data and numerical results by the boundary element method (BEM) indicates the correctness of the present EMM. Four aspects involving varying height of the sill, varying width of the sill, varying water depth of the right semi-infinite subdomain, and varying relative positions between the buoy and the sill are considered. Analytical results show that among all the hydrodynamic coefficients, the added mass coefficient of heave is affected most by the varying sill.

Modified Kawahara equation within a fractional derivative with non-singular kernel

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

Non-linear water waves (KdV) equation by Painlevé property and Schwarzian derivative

The Korteweg-de Vries (KdV) equation, a nonlinear partial differential equation which describes the motion of water waves, has been of interest since John Scott Russell (1834) [4]. In present work we study this kind of equation and through our study we found that the KdV equation passes Painleve?s test, but we could not locate the solution directly, so we used Schwarzian derivative technique. Therefore, we were able to find two new exact solutions to the KdV equation. Also, we used the numerical method of Modified Zabusky-Kruskal to describe the behavior of these solutions.

Cloaking a vertical cylinder via homogenization in the mild-slope equation

We describe a method to construct devices which allows a vertical rigid cylinder to be cloaked for any far-field observer in the case of linear water waves. An adaptation of parameters given by a geometric transform performed in the mild-slope equation is achieved via homogenization. The final device, which respects the physical constraints of the problem, is obtained with a conformal mapping. The result of this algorithm is a structure surrounding the vertical cylinder, composed of an annular region with varying bathymetry and with rigid vertical objects piercing the free surface. An approximate cloaking is achieved, which implies a reduction of the mean drift force acting on the cylinder.