Diffraction and Radiation of Water Waves by a Heaving Absorber in Front of a Bottom-Mounted, V-shaped Breakwater of Infinite Length

In the present study, the problems of diffraction and radiation of water waves by a cylindrical heaving wave energy converter (WEC) placed in front of a reflecting V-shaped vertical breakwater are formulated. The idea conceived is based on the possible exploitation of amplified scattered and reflected wave potentials originating from the presence of V-shaped breakwater, towards increasing the WEC’s wave power absorption due to the wave reflections. An analytical solution based on the method of images is developed in the context of linear water wave theory, taking into account the hydrodynamic interaction phenomena between the converter and the vertical wall. Numerical results are presented and discussed concerning the hydrodynamic forces on the absorber and its wave power efficiency for various examined parameters, namely, the breakwaters’ forming angle, the distance between the converter and the vertical walls and the wave heading angle. The results show that the amount of the harvested wave power by the WEC in front of the walls is amplified compared to the wave power absorbed by the same WEC in the open sea.

WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

Scattering of Gravity Waves by a Rectangular Floating Flexible Porous Plate

Scattering of oblique surface gravity waves by a finite, floating porous-elastic plate is investigated, with assumptions of linear water wave theory and plate response. A boundary value problem is set up, wherein the thin plate equation together with a porosity parameter is used to formulate the condition on the floating plate. A matched eigenfunction approach is adopted for the solution of this problem, with roots of the dispersion relation being located with the aid of contour plots, and various hydrodynamic scattering quantities are computed. Energy dissipation due to plate porosity is seen to have a significant impact on both reflection and transmission of waves, while flexibility of plate only alters the extent of wave reflection by porous elastic plates. An oscillatory trend is shown by reflection coefficient for smaller values of relative plate width, and there is no variation in reflection or transmission coefficients when the plate width is increased beyond a certain cut-off value. Comparison of scattering properties of four different types of plates highlights the effects of porosity and flexibility and establishes the superiority of a flexible porous plate as a wave attenuating device, with moderate reflection, high energy dissipation and low transmission.

Analysis of Wave Action Through Multiple Submerged Porous Structures

Wave interaction with multiple bottom-standing rectangular porous structures of different structural parameters is numerically modeled using the multidomain boundary element method and the matched eigenfunction expansion method, while assuming linear water wave theory. The sensitivity of wave reflection and transmission to the wave and structural parameters is analyzed with the objective to maximize wave energy attenuation. Different configurations of multiple structures are tested for maximizing the efficiency of dissipation. Furthermore, wave trapping by multiple porous structures near a sloping rigid wall is studied. Bragg resonance is observed in the case of wave scattering by multiple structures irrespective of wave and structural parameters and is found as proportional to the number of structures deployed. In addition, the study reveals that in the presence of multiple structures, due to more wave energy dissipation, wave transmission in the lee side of the structures is reduced significantly when compared with that observed for a single structure.

Radiated Force due to Surge Motion by a Pair of Submerged Cylinder in Water

Evaluation of hydrodynamic coefficients due to surge of submerged structure is great significant to designing a device which can be consider as a device of wave energy. In the present work, a theoretical approach is developed to describe radiation of water wave by fully submerged cylinder placed above a submerged circular plate in water of finite depth which is based on linear water wave theory The radiation problem due to surge motion by this pair of cylinders have investigated with the suspicion of linear water wave theory. To determine the radiated potentials in every area, we utilize the eigenfunction expansion method and variables separation method. Finally, we derived the analytical expressions of Hydrodynamic coefficients i. e. added mass and damping coefficient due to surge and associated unknown coefficients are calculated by utilizing the matching conditions between the physical and virtual boundaries. A set of added mass and damping coefficient have presented graphically for various radius of the submerge cylinder.

Approximation Models For Water Wave Equations

In this work we are interested in developing approximate models for water waves equation. We present the derivation of the new equations uses approximation of the phase velocity that arises in the linear water wave theory. We treat the (KdV) equation and similarly the C-H equation. Both of them describe unidirectional shallow water waves equation. At the same time, together with the (BBM) equation we propose, we provide the best approximation of the phase velocity for small wave numbers that can be obtained with second and third-order equations. We can extend the results of [3, 4]. A comparison between the methods is mentioned in this article. Key words: C-H equation, KdV equation, approximation, water wave equation, numerical methods. --------------------------------------------------------------------------------------------------------------------- [3]. D. J. Benney, “Long non-linear waves in fluid flows,” Journal of Mathematical Physics, vol. 45, pp. 52–63, 1966. View at Google Scholar · View at Zentralblatt MATH [4]. Bezati, L., Hajrulla, S., & Hoxha, F. (2018). Finite Volume Methods for Non-Linear Eqs. International Journal of Scientific Research and Management, 6(02), M- 2018.

The Spring-Like Air Compressibility Effect in OWC Wave Energy Converters: Hydro-, Thermo- and Aerodynamic Analyses

The oscillating-water-column (OWC) wave energy converter consists of a hollow (fixed or floating) structure, open to the sea below the water surface. Wave action alternately compresses and decompresses the air trapped above the inner water free-surface, which forces air to flow through a turbine coupled to a generator. The spring-like effect of air compressibility in the chamber is related to the density-pressure relationship. It is known to significantly affect the power performance of the full-sized converter, and is normally not accounted for in model testing at reduced scale. Three theoretical models of increasing complexity are analysed and compared: (i) the incompressible air model; (ii) the isentropic process model; (iii) and the (more difficult and rarely adopted) adiabatic non-isentropic process model in which losses due to the imperfectly efficient turbine are accounted for. The air is assumed as a perfect gas. The hydrodynamic modelling of wave energy absorption is based on linear water wave theory. The validity of the various simplifying assumptions, especially in the aero-thermodynamic domain, is examined and discussed. The validity of the three models is illustrated by a case study with numerical results for a fixed-structure OWC equipped with a Wells turbine subject to irregular waves.

Wave scattering by a fixed submerged platform over a step bottom

This study deals with oblique and normal water wave scattering by a fixed submerged body of rectangular cross section which is infinite in length and finite in width. The fluid domain is considered as infinite as well as semi-infinite in nature. The study is carried out under the assumption of small amplitude linear water wave theory. It is considered that the bottom has a step and the submerged body is considered in shallower water depth region. The velocity potential is derived using the eigenfunction expansion method. The unknown constants, which appear in the expansion formulae, are obtained using orthogonal relation along with the boundary conditions at the interfaces. The wave-induced hydrodynamic forces acting on the submerged body and vertical wall are computed for different geometrical parameters. The wave reflection coefficient and the free surface motion are also calculated to see the wave phenomena around the submerged body.

Existence of edge waves along three-dimensional periodic structures

Existence of edge waves travelling along three-dimensional periodic structures is considered within the linear water-wave theory. A condition ensuring the existence is derived by analysing the spectrum of a suitably defined trace operator. The sufficient condition is a simple inequality comparing a weighted volume integral, taken over the submerged part of an element in the infinite array of identical obstacles, to the area of the free surface pierced by the obstacle. Various examples are given, and the results are extended to edge waves along periodic coastlines and over a periodically varying ocean floor.