Oblique Wave Scattering by a Vertical Flexible Porous Plate (original) (raw)
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Hydroelastic Response of a Flexible Submerged Porous Plate for Wave Energy Absorption
Journal of Marine Science and Engineering, 2020
The application of flexible horizontal porous structure has a significant impact on the design of breakwaters and wave energy absorption devices for coastal protection and wave energy extraction, respectively. This type of structure is more economical compared to a rigid type structure. Therefore, the hydroelastic response of the flexible porous structure can be investigated to widen the influence of structural deformations in design parameters. This paper presents a generalized expansion formula for the said problem based on Green’s function in the water of finite depth (FD) and infinite depth (ID). The series form of the velocity potentials for the wave-maker problem is also derived using Green’s second identity. The derived expansion formula is applied to a real physical problem and the analytical solution is obtained utilizing a matched eigenfunction expansion method under velocity potential decompositions. The convergence study of the series solution is checked. The present res...
Surface wave scattering by porous and flexible barrier over a permeable bed
THE 11TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS
Using small amplitude wave theory, scattering of water waves by a vertical flexible barrier over a porous bed is studied. The boundary value problem in the form of Helmholtz equation is solved by the matched vertical eigenfunction expansion method. By exploiting the continuity of pressure and velocity at the interface along with Darcy's law for porous structure, the obtained coupled relation is solved by least-squares approximation method. The behavior of flexible barrier against the wave action for various physical quantities are studied and the numerical results are discussed. It is observed that due to the porous structure, a tranquility zone is created on the lee side of the barrier.
Ocean Engineering, 2018
An analytical study is presented in this paper for oblique wave scattering by a floating elastic plate in a one or twolayer body of water over a porous seabed of infinite depth. The solution procedure adopted, under the assumption of small-amplitude surface waves and structural response, is the eigenfunction expansion method. The study aims to look into the interaction between oblique waves and a floating elastic plate that serves as an effective breakwater. Effects of three types of edge conditions, viz. (i) free edge, (ii) simple-supported edge, and (iii) clamped edge are analyzed. Numerical results for the reflection and transmission coefficients are computed and examined for various values of the wave, porous bed and structural parameters. Results for wave interaction with an elastic plate over a non-porous bed are obtained as special cases and compared with results available in the literature. The study reveals that for various combinations of wave and structural parameters, zero reflection and full transmission may occur in case of rigid bottom and real porous-effect parameter of the porous bed. However, for complex porous-effect parameter, zero reflection and full transmission do not occur. Moreover, due to the energy dissipation by porous bed, wave transmission decreases significantly with increase in length of the floating plate in case of complex porous-effect parameter. The results will be useful in the design of breakwaters for the protection of harbors, inlets and beaches against attacks from surface waves.
Water wave scattering by an elastic plate floating in an ocean with a porous bed
Applied Ocean Research, 2014
The problem of water wave scattering by a thin horizontal elastic plate (semi-infinite as well as finite) floating on an ocean of uniform finite depth in which the ocean bed is composed of porous material of a specific type is analyzed. The method of eigenfunction expansion is used in the mathematical analysis and the quantities of physical interest, namely the reflection and transmission coefficients, are obtained. Numerical estimates for these coefficients are obtained for different values of the parameter describing the porosity of the ocean bed and for different edge conditions of the elastic plate. The edge conditions considered here involve (i) a free edge, (ii) a simply supported edge and (iii) a built-in edge. From the numerical results it is observed that for free edge condition, the porosity of the ocean bed has little effect on the reflection and transmission coefficient for both the cases of semi-infinite and finite elastic plate. The energy identity related to reflection and transmission coefficients in a porous bed is derived and is used as a partial check on the correctness of the numerical results for the semi-infinite elastic plate.
Coastal Engineering Journal, 2016
A semi-analytic model is presented for oblique wave scattering by a bottom-standing or surface-piercing flexible porous barrier in water of finite depth with a step-type bottom topography. The physical problem is solved using the methods of least-squares and multimode approximation associated with the modified mild-slope equation. Effects on the wave scattering due to bed profile, structural rigidity, compressive force, angle of incidence, barrier length, porosity, and height of the step are examined. The study reveals that under some special conditions, nearly zero/full reflection may occur in the case of wave scattering by a partial flexible porous barrier in the presence of an undulated bottom topography. Further, the study predicts that the Bragg resonance may not occur in the case of wave scattering by a topography of sinusoidal profile. The present study provides insights to help understand how waves are transformed in a marine environment with/without flexible porous barriers in the presence of a bottom topography. The concept and methodology can be generalized to analyze problems of similar nature arising in ocean engineering.