Water wave radiation by a submerged rough disc

A thin circular body is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the boundary of the body. Using a perturbation method, the problem is then reformulated by a sequence of simpler hypersingular equations over a flat disc making it well suited for an efficient previously used solution method. The first order approximation is computed and the hydrodynamic force due to heaving radiation motion are presented in terms of the added mass and damping coefficients for a polynomial cap and for a rough disc, modelled by a superposition of sinusoidal surfaces defined by randomly generated parameters. The solution exhibits larger maxima associated with smaller volume of submergence of the body. A slight shift of the damping coefficient maxima to lower frequencies is noticed for the caps. Rough discs with similar statistical properties exhibit different behaviours. Thus, it is the exact specific form of the rough disc that dictates the hydrodynamic force.     

Effects of flexible bottom on radiation of water waves by a sphere submerged beneath an ice-cover

Meccanica - A particular hydro-elastic model is considered to examine a radiation problem involving an immersed sphere in an infinitely extended ice-covered sea, where the lower surface is...     

Water wave scattering by a submerged circular-arc-shaped plate

The problem of water wave scattering by a thin circular-arc-shaped plate submerged in infinitely deep water is investigated by linear theory. The circular-arc is not necessarily symmetric about the vertical through its center. The problem is formulated in terms of a hypersingular integral equation for a discontinuity of the potential function across the plate. The integral equation is solved approximately using a finite series involving Chebyshev polynomials of the second kind. The unknown constants in the finite series are determined numerically by using the collocation and the Galerkin methods. Both the methods ultimately produce very accurate numerical estimates for the reflection coefficient. The numerical results are depicted graphically against the wave number for a variety of configurations of the arc. Some results are compared with known results available in the literature and good agreement is achieved. The suitability of using a circular-arc-shaped plate as an element of a water wave lens has also been discussed on the basis of the present numerical results.     

Water surface wave radiation generated by multiple cylinders oscillating with identical frequency

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Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement

The dynamic response of submerged and confined disk-like structures is of interest in engineering applications, such as in hydraulic turbine runners. This response is difficult to be estimated with accuracy due to the strong influence of the boundary conditions. Small radial gaps as well as short axial distances to rigid surfaces greatly modify the dynamic response because of the added mass and damping effects.In this paper, the influence of the axial nearby rigid distance on the dynamic response of a submerged disk is evaluated when the radial gap is very small. Moreover, the effects of the fluid depth and fluid viscosity on the natural frequencies and damping ratio of the submerged disk are studied. The study has been performed experimentally and numerically using structural–acoustic simulations.For the experimental investigation a test rig has been developed. It consists of a disk attached to a shaft and confined with a small radial gap inside a cylindrical container full of water. The disk can be moved up and down along the shaft to vary the axial distance to the nearby rigid surface. Piezoelectric patches are used to excite the disk and the response is measured with submersible accelerometers. Several excitation patterns can be used due to the disposition of these piezoelectric patches. For each configuration tested, the dynamic response of the structure is studied analyzing the natural frequencies and damping ratio of the disk attached to the shaft. The numerical results have been compared with the experimental results.     

Unsteady drag on a sphere by shock wave loading

The dynamic drag coefficient of a sphere by shock wave loading is investigated numerically and experimentally. The diameter of the sphere is varied from 8 m to 80 mm in numerical simulation. The axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved. The numerical result is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube. It is found that the sphere experiences in the early interaction one order higher drag than in the steady state. A transient negative drag, mainly resulting from the focusing of shock wave on the rear side of the sphere, is observed only for high Reynolds number flows, and the drag becomes positive because of increased skin friction for low Reynolds number flows.Received: 10 March 2004, Accepted: 24 May 2004, Published online: 20 August 2004[/PUBLISHED]M. Sun: Send offprints requests to     

Water wave interaction with a sphere in a two-layer fluid flowing through a channel of finite depth

Using linear water wave theory, we consider a three-dimensional problem involving the interaction of waves with a sphere in a fluid consisting of two layers with the upper layer and lower layer bounded above and below, respectively, by rigid horizontal walls, which are approximations of the free surface and the bottom surface; these walls can be assumed to constitute a channel. The effects of surface tension at the surface of separation is neglected. For such a situation time-harmonic waves propagate with one wave number only, unlike the case when one of the layers is of infinite depth with the waves propagating with two wave numbers. Method of multipole expansions is used to find the particular solutions for the problems of wave radiation and scattering by a submerged sphere placed in either of the upper or lower layer. The added-mass and damping coefficients for heave and sway motions are derived and plotted against various values of the wave number. Similarly the exciting forces due to heave and sway motions are evaluated and presented graphically. The features of the results find good agreement with previously available results from the point of view of physical interpretation.     

Free vibration analysis of a hung clamped-free cylindrical shell partially submerged in fluid

The free flexural vibration of a hung clamped-free cylindrical shell partially submerged in a fluid is investigated. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modelled by using the Rayleigh-Ritz method based on Sanders’ shell theory. The kinetic energy of the fluid is derived by solving the boundary-value problem related to the fluid motion. The natural vibration characteristics of the partially submerged cylindrical shell are discussed with respect to the added virtual mass approach. In this study, the nondimensionalized added virtual mass incremental factor for the partially submerged finite shell is derived. This factor can be readily used to estimate the change in the natural frequency of the shell due to the presence of a fluid.     

Deformation and regimes of liquid column during water exit of a partially submerged sphere using the front-tracking lattice Boltzmann method

When a solid sphere exits water at a given velocity, the liquid column is pulled out of a liquid reservoir. The present study focuses on the dynamic deformation of the liquid column and on the identification of the liquid column regime on the Weber number and dimensionless time (We-t*) map. The three-dimensional model of water exit has been established on the basis of the lattice Boltzmann method. A mass tracking algorithm was incorporated to capture the free surface, where the liquid–gas​ two-phase flow is simplified to a single-phase free surface flow. The surface tension is included by adding a perturbation term and the gravity as a body force is introduced in form of calculating the equilibrium distribution with an altered velocity. The contact angle condition in numerical simulation is not considered. The accuracy of the numerical results is demonstrated through the comparisons with the prior numerical and the experimental results in the literature. A parametric study has been conducted numerically on the radius and volume and of liquid column. Besides, the relationship between the pinch-off time of a liquid column and the Froude number has been obtained. Moreover, the evolution of the liquid column shape with a wide range of the Weber number and time scales are discussed based on the number of ligaments and droplets. The liquid column exhibits different characteristics and has been divided into three regimes. The transition between different regimes has been analyzed and the critical Weber number is given.     

Gravity wave radiation from unsteady rotational flow in an f-plane shallow water system

Spontaneous gravity wave radiation from an unsteady rotational flow is investigated numerically in an f-plane shallow water system. Unlike the classical Rossby adjustment problem, where free development of an initially unbalanced state is investigated, we consider development of a barotropically unstable zonal flow which is initially balanced but maintained by zonal mean forcing. Gravity waves are continuously radiated from a nearly balanced rotational flow region even when the Froude number is so small that balance dynamics is thought to be a good approximation for the full system. The source of gravity waves is discussed by analogy with the theory of aero-acoustic sound wave radiation (the Lighthill theory). It is shown that the source regions correspond to regions of strong rotational flow. The gradual change of rotational flow causes gravity wave radiation. We propose an approximation for these strong sources on the assumption that the dominant flow in the jet region is non-divergent rotational flow. In addition, we calculate the zonally symmetric component of gravity waves far from the source regions, solving the Lighthill equation. Using scaling analyses for perturbations, these gravity waves can be calculated with only one approximated source term that is related to the latitudinal gradient of the fluid depth and the latitudinal mass flux. In spite of its simplicity, this approximation not only explains the physical cause of gravity wave radiation, but gives an amount of source close to that obtained by classical approximation derived from vortical motion.     

Water waves generated due to initial axisymmetric disturbances in water with an ice-cover

This paper is concerned with the generation of water waves due to prescribed initial axisymmetric disturbances in a deep ocean with an ice-cover modelled as a thin elastic plate. The initial disturbances are either in the form of an impulsive pressure distributed over a certain region of the ice-cover or an initial displacement of the ice-cover. Assuming linear theory, the problem is formulated as an initial-value problem in the velocity potential describing the ensuing motion in the fluid. In the mathematical analysis, the Laplace and Hankel transform techniques have been utilised to obtain the deformation of the ice-covered surface as an infinite integral in each case. The method of stationary phase is used to evaluate the integral for large values of time and distance. Figures are drawn to show the effect of the presence of ice-cover on the wave motion.     

Effect of acoustic radiation on a spherical drop of liquid

The effect of radiation force on a drop of liquid in an acoustic field is examined. It is established that the force depends on the ratio of the densities of the liquid and the drop and on their adiabatic elastic moduli __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 26–34, July 2007.     

Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure

The shedding and evolution of the vortical structures generated by a solitary wave propagating over a submerged cylindrical structure are investigated experimentally and numerically. The cylindrical structure consists of two concentric cylinders and represents a simplified model for an offshore submerged intake structure typically used in coastal power plants. Flow visualization by dye injection is used to identify the dominant vortical structures near the structure. The flow visualization results show an unexpected flow reversal that causes shedding of secondary vortical structures. The experimental results are used to check a three-dimensional volume of fluid-large eddy simulation (VOF-LES) numerical model. The VOF-LES model is then used to further study the flow structure. A total of six dominant vortical structures generated by the wave motion are identified, followed by two more generated by the flow reversal. In summary, this paper provides the vorticity evolution for a complex fluid–structure interaction problem and a three-dimensional numerical simulation tool has also been validated, which can be extended to study more complex geometries and wave conditions.     

Mathematical study on wave interaction with a composite poroelastic submerged breakwater

In this paper the problem of wave propagation over an adjoining-type of composite submerged poroelastic breakwater with different materials is investigated theoretically. A new analytical solution for describing the dynamic response of wave interaction with poroelastic structures is presented. A set of simultaneous equations is developed and numerically solved in order to produce a general solution for each region subject to matching boundary conditions. The present paper focuses on the changes of influence parameters such as different component widths of the composite breakwater, permeability coefficients, composite materials and configurations of breakwater on wave variations.     

Effects of dynamic viscoelastic properties on acoustic diffraction by a solid sphere submerged in a viscous fluid

Summary  This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a homogeneous, isotropic, viscoelastic, solid sphere immersed in an unbounded viscous, heat-nonconducting, compressible fluid. The dynamic viscoelastic properties of the spherical scatterer and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak–Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic quantities such as the scattered far-field pressure directivity pattern, scattered intensity distribution, differential scattering cross section, and the acoustic radiation force are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the solid obstacle can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established. Received 15 January 2002; accepted for publication 2 July 2002 The authors wish to sincerely thank professors Daniel Levesque, Roderic Lakes, Yves Berthelot, S. Temkin, and Andrei Dukhin for valuable and productive consultations on dynamic theory of viscoelasticity and acoustics of (thermo)viscous media.     

Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow

A three-dimensional rarefied-gas flow past a spinning sphere in the transitional and near-continuum flow regimes is studied numerically. The rarefaction and compressibility effects on the lateral (Magnus) force and the aerodynamic torque exerted on the sphere are investigated for the first time. The coefficients of the drag force, the Magnus force, and the aerodynamic torque are found for Mach numbers ranging from 0.1 to 2 and Knudsen numbers ranging from 0.05 to 20. In the transitional regime, at a certain Knudsen number depending on the Mach number the Magnus force direction changes. This change is attributable to the increase in the role of normal stresses and the decrease in the contribution of the shear stresses to the Magnus force with decrease in the Knudsen number. A semi-empirical formula for the calculation of the Magnus force coefficient in the transitional flow regime is proposed.     

Scattering of water waves by inclined thin plate submerged in finite-depth water

Summary  The problem of water wave scattering by an inclined thin plate submerged in water of uniform finite depth is investigated here under the assumption of irrotational motion and linear theory. A hypersingular integral equation formulation of the problem is obtained by an appropriate use of Green's integral theorem followed by utilization of the boundary condition on the plate. This hypersingular integral equation involves the discontinuity in the potential function across the plate, which is approximated by a finite series involving Chebyshev polynomials. The coefficients of this finite series are obtained numerically by collocation method. The quantities of physical interest, namely the reflection and transmission coefficients, force and moment acting on the plate per unit width, are then obtained numerically for different values of various parameters, and are depicted graphically against the wavenumber. Effects of finite-depth water, angle of inclination of the plate with the vertical over the deep water and vertical plate results for these quantities are shown. It is observed that the deep-water results effectively hold good if the depth of the mid-point of the submerged plate below the free surface is of the order of one-tenth of the depth of the bottom. Received 30 November 2000; accepted for publication 26 June 2001     

Numerical simulation of a solitary wave interaction with submerged multi-bodies

The problems of a solitary wave passing over rectangular cylinders have been analysed. The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method. The free surface is dealt with by the Volume of Fluid method (VOF). Results for a solitary wave passing over a single cylinder are compared with the experimental data of Seabra-Santos, Penouard and Temperville^[2] and better agreement is obtained than those obtained from the long wave equation based on the potential flow theory. Results are also given for two cylinders with different gaps. The project supported by the National Natural Science Foundation of China and the Development Foundation of Science and Technology of Shanghai Education Committee and the Royal Society.     

基于扰动方程的超音速轴对称射流马赫波辐射研究

超音速不稳定波是导致剪切流失稳和转捩的主要不稳定模态,这种模态以马赫波的形式辐射到远场,从而产生强烈的声场。采用线性稳定性理论和非线性扰动方程(NLDE)分析,计算超音速轴对称射流不稳定波的扰动演化(Ma=2.1),对马赫波辐射进行研究,包括马赫波辐射方向、辐射源位置,以及随斯特劳哈尔数的变化情况。研究结果表明,在超音速轴对称射流中,马赫波沿固定方向辐射向远方,不稳定波相位沿另一方向传播,这两个方向相互正交;马赫波辐射源位置位于不稳定波压力幅值最大处;斯特劳哈尔数St越大,马赫波辐射的能力越强,辐射区域越集中。