Bragg scattering of waves propagating over a series of poro-elastic submerged breakwaters

This paper presents a mathematical study for the Bragg scattering of water waves propagating over a series of rectangular poro-elastic submerged breakwaters. Based on the linear wave theory and the improved Biot's theory of poro-elastic media with suitable matching conditions, an analytical solution was obtained as a function of elasticity, permeability and geometry of the submerged breakwaters. Experiments were also conducted in a wave flume to verify the present analytical study. In addition, the Bragg resonances for different influence parameters were studied. Satisfactory agreement between the theoretical predictions and the laboratory observations demonstrates the applicability of the present analytical result.     

非平整、多孔介质海底上波浪传播的复合方程

为了反映近岸区域实际存在的多孔介质海底效应，并且考虑到波浪在刚性海底上传播模型的 最新研究进展，运用Green第二恒等式建立了波浪在非平整、多孔介质海底上传播的复合方 程. 假设水深和多孔介质海底层厚度均由两种分量组成：慢变分量，其水平变化的长度尺度大于 表面波的波长；快变分量，其水平变化的长度尺度与表面波的波长等阶，但其振幅小于表面 波的振幅. 另外，多孔介质层下部边界的快变分量比水深的快变分量小1个量级. 针对水体层和多孔介质层，选择Green第二恒等式方法给出了波浪传播和渗透的复合方程， 它在交接面上满足压力和垂直渗透速度的连续性条件,可充分考虑波数变化的一般连续性， 并包含了某些著名的扩展型缓坡方程.     

The scattering of vorticity waves by a supersonic rectangular wing

We consider the scattering of incident vorticity waves by a rigid rectangular wing in supersonic flow, and complete the solution of the problem using the modified Wiener-Hopf technique. The new feature of this analysis is the inclusion of a finite chord and a finite span in an analytical solution, and the nature of both the unsteady lift and the far-field radiation are examined in some detail. We find in particular that for large gust sweep angles the finite span can have a significant effect on the lift distribution away from the central part of the span, and that increasing the gust sweep produces a marked reduction in the level of acoustic energy generated by the interaction.     

On the scattering of spherical waves by a cylindrical object

Summary The connection between plane wave and spherical wave scattering from an infinitely cylindrical object is investigated. If the distance of the source and the observer from the axis of the cylinder are denoted by ϱ₀ and ϱ, respectively, the ratio of the scattered field to that for plane wave excitation [ϱ0/(ϱ0 + ϱ)]^1/2.     

Propagation of plane surface waves over a rectangular step with overhang and over a partially capped rectangular trench

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 40–46, September–October, 1991.     

On the interaction of water waves and seabed by the porous medium model

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results. The project supported by the National Science Foundation of China     

Wave scattering by a floating porous elastic plate of arbitrary shape: A semi-analytical study

In this paper, a semi-analytical model based on linear potential flow theory and an eigenfunction expansion method is developed to study wave scattering by a porous elastic plate with arbitrary shape floating in water of finite depth. The water domain is divided into the interior and exterior regions, corresponding to the domain beneath the plate and the rest extending towards infinite distance horizontally, respectively. The unknown coefficients in the potential expressions are determined by satisfying the continuity conditions for pressure and velocity at the interface of the two regions, together with the conditions for the motion/force at the edge of the plate, where the Fourier series expansion method is employed to deal with the terms associated with the radius function. A plate with three shapes – circular, cosine and elliptical – and three edge conditions are considered. We find that the largest deflection of the plate with a simply supported edge and a clamped edge is more sensitive to the change in porosity when the porosity is small. The power dissipated by an elliptical plate with its major axis perpendicular to the incident wave direction is the largest among the case studies for the majority of the porosity values tested.     

Complex variable function method for the scattering of plane waves by an arbitrary hole in a porous medium

Based on the complex variable function method, a new approach for solving the scattering of plane elastic waves by a hole with an arbitrary configuration embedded in an infinite poroelastic medium is developed in the paper. The poroelastic medium is described by Biot's theory. By introducing three potentials, the governing equations for Biot's theory are reduced to three Helmholtz equations for the three potentials. The series solutions of the Helmholtz equations are obtained by the wave function expansion method. Through the conformal mapping method, the arbitrary hole in the physical plane is mapped into a unit circle in the image plane. Integration of the boundary conditions along the unit circle in the image plane yields the algebraic equations for the coefficients of the series solutions. Numerical solution of the resulting algebraic equations yields the displacements, the stresses and the pore pressure for the porous medium. In order to demonstrate the proposed approach, some numerical results are given in the paper.     

Ice-water convection in an inclined rectangular cavity filled with a porous medium

This paper reports on the results of a numerical study on the equilibrium state of the convection of water in the presence of ice in an inclined rectangular cavity filled with a porous medium. One side of the cavity is maintained at a temperature higher than the fusion temperature while the opposite side is cooled to a temperature lower than the fusion temperature. The two remaining sides are insulated. Results are analysed in terms of the density inversion parameter, the tilt angle, and the cooling temperature. It appears that the phenomenon of density inversion plays an important role in the equilibrium of an ice-water system when the heating temperature is below 20°. In a vertical cavity, the density inversion causes the formation of two counterrotating vortices leading to a water volume which is wider at the bottom than at the top. When the cavity is inclined, there exist two branches of solutions which exhibit the bottom heating and the side heating characteristics, respectively (the Bénard and side heating branches). Due to the inversion of density, the solution on the Bénard branch may fail to converge to a steady state at small tilt angles and exhibits an oscillating behavior. On the side heating branch, a maximum heat transfer rate is obtained at a tilt angle of about 70° but the water volume was found to depend very weakly on the inclination of the cavity. Under the effect of subcooling, the interplay between conduction in the solid phase and convection in the liquid leads to an equilibrium ice-water interface which is most distorted at some intermediate cooling temperature.     

Deformation of a thick-wall cylindrical shell with a porous filler under an internal blast loading

Hydromechanics Institute, National Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 9, pp. 61–65, September, 1995.     

Multichannel resonant scattering theory applied to the acoustic scattering by an eccentric elastic cylindrical shell immersed in a fluid

The multichannel resonant scattering theory is developed in the field of the acoustic scattering. Because it takes into account mode conversions, this theory deals with a nondiagonal scattering S matrix. It is used here for the study of the acoustic scattering by an elastic eccentric shell. In this case the mode conversions are due to the fact that the Lamb type waves propagating around the shell are submitted to a reflection-refraction phenomenon when passing through the thinner part of the shell. All informations on the resonances are provided by the study of Argand's diagrams. In particular, the partition of the resonant energy over all the vibration modes of the scatterer is obtained. A numerical validation of the multichannel resonant scattering theory is then given. We focus our attention on the bifurcation of resonances, and the existence of angular diagrams with an odd numbers of lobes; both are due to mode conversions. Experiments have been performed which are in agreement with the theoretical results.     

Stability of dual solutions in stagnation-point flow and heat transfer over a porous shrinking sheet with thermal radiation

An analysis is carried out to study the steady two-dimensional stagnation-point flow and heat transfer of an incompressible viscous fluid over a porous shrinking sheet in the presence of thermal radiation. A set of similarity transformations reduce the boundary layer equations to a set of non-linear ordinary differential equations which are solved numerically using fourth order Runge-Kutta method with shooting technique. The analysis of the result obtained shows that as the porosity parameter β increases, the range of region of existence of similarity solution increases. It is also observed that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on β. We then discuss the stability of the unsteady solutions about each steady solution, showing that one steady state solution corresponds to a stable solution whereas the other corresponds to an unstable solution. The stable solution corresponds to the physically relevant solution. Further we obtain numerical results for each solution, which enable us to discuss the features of the respective solutions.     

Rayleigh-type waves in a water-saturated porous half-space with an elastic plate on its surface

The paper deals with the plane problem of steady-state time harmonic vibrations of an infinite elastic plate resting on a water-saturated porous solid. The displacements of the plate are described by means of the linear theory of small elastic oscillations. The motion of the two-phase medium is studied within the framework of Biot's linear theory of consolidation. The main interest is focused on the investigation of properties of the Rayleigh-type waves propagating alongside of the contact surface between the plate and the porous half-space. In particular, the dependence of the phase velocity and attenuation of the waves on the plate stiffness, mass coupling coefficient, and degree of saturation of the medium is studied. Besides, for the limiting case of an infinitely thin plate, the comparison of the wave characteristics is carried out with those of the pure Rayleigh waves.     

Flow over rectangular porous block in a fixed width channel: influence of porosity and aspect ratio

Flow over a rectangular porous block placed in a fixed width channel is considered and the influence of block aspect ratio on the heat transfer rate from the block is examined. A non-porous solid block is also accommodated to compare the effect of porosity on the flow field and heat transfer characteristics. Aspect ratio and the porosity of the block are varied in the simulations. A numerical scheme employing a control volume approach is considered when predicting the flow and temperature fields. The Reynolds number is selected to yield the mix convection situation in the flow field. It is found that the aspect ratio significantly influences Nu and Gr numbers, in which case increasing the aspect ratio enhances Nu while lowering Gr. Increasing porosity improves the heat transfer rates from the porous block, provided that at high aspect ratios, this situation ceases due to blockage effect of the body in the channel.     

Diffraction of plane waves by an infinitely long elastic rod floating on the surface of a liquid

The interaction of plane waves coming from infinity with an infinitely long elastic rod floating on the surface of a liquid is considered. The liquid is assumed to be ideal and have infinite depth. It is assumed that the rod cannot become separated from the liquid. The parameters of the waves that pass through the rod and are reflected from it are determined, and the force factors in the transverse sections of the rod are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 62–67, September–October, 1980.     

Reflection and transmission of regular water waves by a thin,floating plate

Measurements of the wave fields reflected and transmitted by a thin floating plastic plate are reported for regular incident waves over a range of incident periods (producing wavelengths comparable to the plate length) and steepnesses (ranging from mild to storm-like). Two different plastics are tested, with different densities and mechanical properties, and three different configurations are tested. The configurations include freely floating plates, loosely moored plates (to restrict drift), and plates with edge barriers (to restrict waves overwashing the plates). The wave fields reflected and transmitted by plates without barriers are shown to become irregular, as the incident waves become steeper, particularly for the denser plastic and the moored plate. Further, the proportion of energy transmitted by the plates without barriers is shown to decrease as the incident wave becomes steeper, and this is related to wave energy dissipation.     

Numerical study of axisymmetric waves in an elastic cylindrical shell partially filled with a viscous liquid

Moscow Institute of Electronics and Mechanical Engineering. Translated from Prikladnaya Mekhanika, Vol. 24, No. 2, pp. 50–54, February, 1988.     

Water wave propagation over multiple porous barriers with variable porosity in the presence of an ice cover

Meccanica - A semi-analytical method is applied to investigate the propagation of flexural wave over multiple bottom-standing porous barriers with variable porosity beneath an ice cover under the...