Scattering of Surface Water Waves Involving Semi-infinite Floating Elastic Plates on Water of Finite Depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Wavefront modulation of water surface wave by a metasurface

We design a planar metasurface to modulate the wavefront of a water surface wave（WSW） on a deep sub-wavelength scale. The metasurface is composed of an array of coiling-up-space units with specially designed parameters, and can take on the work of steering the wavefront when it is pierced into water. Like their acoustic counterparts, the modulation of WSW is ascribed to the gradient phase shift of the coiling-up-space units, which can be perfectly tuned by changing the coiling plate length and channel number inside the units. According to the generalized Snell＇s law, negative refraction and ＇driven＇ surface mode of WSW are also demonstrated at certain incidences. Specially, the transmitted WSW could be efficiently guided out by linking a symmetrically-corrugated channel in ＇driven＇ surface mode. This work may have potential applications in water wave energy extraction and coastal protection.

WATER SURFACE WAVE RADIATION GENERATED BY MULTIPLE CYLINDERS OSCILLATING WITH IDENTICAL FREQUENCY

The water surface wave radiation problem caused by multiple cylinders oscillating with identical frequency was solved in frequency domain by the boundary element method using simple Green's function in the inner water region combined with the eigenfunction expansions in the outer water region. The numerical method is suitable to the situation of constant depth of outer regions and complicated boundary conditions of inner region, while the oscillating modes, motion amplitudes and phases of the cylinders may be different from one another. The second order potential and hydrodynamic forces acting on each cylinder were evaluated completely by perturbation method. Compared with the case of single oscillating cylinder, hydrodynamic interference phenomena, such as wave resonance and negative added mass, of the radiation problem due to the oscillatory motions of multiple cylinders are identified which is of engineering importance to the design of moorings and other facilities involving multiple structures.

Measuring method of water surface wave relaxation rate based on linear array CCD

Relaxation rate is a very crucial parameter in physics.For the water surface wave,its relaxation rate is directly relevantto the response time of disturbed spectrum returning back to its quasi-steady state.It is difficult to be calculated directly asa function of different oceanographic and meteorological parameters.Previous researches were mainly based on experimentalmeasurements or parameterization.In this paper,a method based on the liner array charge-coupled device(CCD)is proposed tomeasure the relaxation rate of the water surface wave.Compared with the traditional methods?it can obtain the information ofsurface wave and current synchronously,and works well under a multi wind-wave environment.Wind wav^tank experimentswere carried out based on this method.The good consistency between the results calculated by this method and the traditionalrelaxation rate models shows the validity of the proposed method.This method can be further used to study the modulation theoryof surface waves by currents.

Proof of Six-Wave Resonance Conditions of Ocean Surface Gravity Waves in Deep Water

A necessary big step up in the modern water wave theories and their widespread application in ocean engineering is how to obtain 6-wave resonance conditions and to prove it. In the light of the existing forms and characteristics of 3-wave, 4-wave and 5-wave resonance conditions, the 6-wave resonance conditions are proposed and proved for currently a maximum wave-wave resonance interactions of the ocean surface gravity waves in deep water, which will be indispensable to both the Kolmogorov spectrum of the corresponding universal wave turbulence and a synthetic 4-5-6-wave resonant model for the ocean surface gravity waves.

Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms

The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.

An Alternative Method to Study Wave Scattering by Semi-infinite Inertial Surfaces

A new method to solve the boundary value problem arising in the study of scattering of two-dimensional surface water waves by a discontinuity in the surface boundary conditions is presented in this paper. The discontinuity arises due to the floating of two semi-infinite inertial surfaces of different surface densities. Applying Green＇s second identity to the potential functions and appropriate Green＇s functions, this problem is reduced to solving two coupled Fredholm integral equations with regular kernels. The solutions to these integral equations are used to determine the reflection and the transmission coefficients. The results for the reflection coefficient are presented graphically and are compared to those obtained earlier using other research methods. It is observed from the graphs that the results computed from the present analysis match exactly with the previous results.

EXPERIMENTAL STUDY ON DARCY′S LAW IN HELE-SHAW CELLS

The basic physics of unsteady Hele-Shaw flow at high Reynolds numbers is mainly studied by an experimental measurement. In order to confirm the Darcy′s law in Hele-Shaw cell, since there is an analogy between flow in cells and that in porous media, progressive water waves are utilized to build an unsteady flow in a Hele-Shaw cell, and which complex wave number is measured by a wave height gauge. Meanwhile, theoretical analyses are used to compare with experimental data. Result shows Darcy′s Law is not exactly correct for unsteady Hele-Shaw flows, and it is expected to conduct a modified Darcy′s Law.