Diffraction of surface waves by a wedge

This paper presents a study of diffraction of surface waves by a wedge with angle . (2–n/m), where n and m are natural numbers and n/m2. The infinitely deep heavy liquid is considered ideal. Two cases are considered: 1) there is a source within the liquid which acts periodically with the frequency and maximal intensity Q; 2) at some point of the liquid surface at the initial instant of time there is a concentrated elevation of volume S. For both cases the exact solution is obtained and asymptotic estimates are made.The author wishes to thank S. S. Voit for guidance and assistance in carrying out the present Investigation.     

Diffraction of waves at finite bodies of revolution

Conclusion The results presented in here permit us to construct approximate solutions of problems of steady-state diffraction of waves of different physical nature at finite bodies of revolution. In each approximation the problems reduce to the problems of diffraction in a spherical system of coordinates with the right sides of the boundary conditions changing in each approximation and with identical homogeneous wave equations in all the approximations.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 9, No. 7, pp. 10–18, July, 1973.     

Diffraction of surface waves by floating elastic plates

Based on the dynamical theories of water waves and Mindlin thick plates, the diffraction of surface waves by a floating elastic plate is presented by using the Wiener–Hopf technique. Firstly, the problem is related to a wave guide in water of finite depth, which is analysed to determine the poles. The resulting hybrid boundary value problem is reduced to solving an infinite system of linear algebraic equations. The results obtained are compared with those calculated by an alternative analysis, and with experimental data. Finally, the effects of the geometric and physical parameters on the distribution of deflection and bending moments in plates are analysed and discussed.     

Diffraction of unsteady gravity waves on a wedge

We consider the occurrence and diffraction on a wedge of gravity waves which appear on the surface of an ideal incompressible liquid as a result of the activation of a periodically acting source. An exact solution is obtained. The time of the transient response is determined. Asymptotic formulas are established for the height of the free liquid surface, which are applicable for any instant of time.The author wishes to thank S. S. Voit for his guidance and assistance in carrying out this study.     

Diffraction of acoustic waves by two nonparallel circular cylinders

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Frikladnaya Mekhanika, Vol. 25, No. 1, pp. 43–51, January, 1989.     

Diffraction of solitary water waves around three-dimensional floating bodies

By using the matched asymptotic expansion method and the idea of edge layer, a mathematic model for describing the interaction between weakly nonlinear shallow-water waves and three-dimensional floating bodies is formed in the paper. As a numerical example, the diffraction of a solitary wave around a vertically floating circular cylinder has been investigated and the results are presented. The present method can further be extended to the study of wave diffraction around floating bodies of general shape. The project is supported by the National Natural Science Foundation of China.     

Diffraction of time-harmonic elastic waves by a cylindrical obstacle

The diffraction of two-dimensional elastic waves by a cylindrical obstacle is investigated. In two-dimensional wave motions, the geometrical configuration as well as the field quantities involved are assumed to be independent of one of the Cartesian coordinates. As such, the two-dimensional theory can be considered as a special case of the three-dimensional one. Following this line of reasoning, the integral-equation formulation of two-dimensional elastodynamic diffraction problems is derived. For a number of configurations, the resulting integral equations are solved numerically. Also, numerical results pertaining to normalized power scattering characteristics and extinction cross-sections are presented.The research reported in this paper has been supported by the Netherlands organization for the advancement of pure research (Z.W.O.).     

Diffraction of surface waves on an inhomogeneous elastic plate

The oblique incidence of small-amplitude waves on an elastic semi-infinite composite plate floating on the free surface of finite-depth water is studied. The front part of a constant-width plate is highed to the basic part and has characteristics different from those of the basic part. The reflection and transmission coefficients of the waves and the vertical displacements of the plate are determined. It is shown that the heterogeneity of the plate material exerts a strong effect on surface-wave diffraction. Methods for decreasing the elastic deformations of the basic part of the plate are proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 42–48, July–August, 2000.     

环形激波绕射、反射和聚焦流场的间断有限元模拟

采用间断有限元方法对环形激波在圆柱形激波管内绕射、反射和聚焦流场进行了数值模拟。将二维守恒方程的间断有限元方法发展到轴对称Euler方程,并对环形激波绕后台阶流动进行了数值计算。计算结果表明,采用间断有限元方法能够有效地捕捉运动激波在圆柱形激波管内传播的复杂流场结构;在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力,在聚焦点附近不会产生振荡或抹平间断现象。     

Diffraction of cnoidal waves by vertical cylinders in shallow water

Diffraction of nonlinear waves by single or multiple in-line vertical cylinders in shallow water is studied by use of different nonlinear, shallow-water wave theories. The fixed, in-line, vertical circular cylinders extend from the free surface to the seafloor and are located in a row parallel to the incident wave direction. The wave–structure interaction problem is studied by use of the nonlinear generalized Boussinesq equations, the Green–Naghdi shallow-water wave equations, and the linearized version of the shallow-water wave equations. The wave-induced force and moment of the Green–Naghdi and the Boussinesq equations are presented when the incoming waves are cnoidal, and the forces are compared with the experimental data when available. Results of the linearized equations are compared with the nonlinear results. It is observed that nonlinearity is very important in the calculation of the wave loads on circular cylinders in shallow water. The variation of wave loads with wave height, wavelength and the spacing between cylinders is studied. Effect of the neighboring cylinders, and the shielding effect of upwave cylinders on the wave-induced loads on downwave cylinders are discussed.