On the Second-Order Wave Radiation of an Oscillating Vertical Circular Cylinder in Finite-Depth Water

1996 ◽  
Vol 40 (03) ◽  
pp. 224-234
Author(s):  
Ömer Gören
Keyword(s):  
Circular Cylinder ◽  
Surface Condition ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Second Order ◽  
Field Analysis ◽  
Wave Number ◽  
Wave Radiation ◽  
Integral Theorem ◽  
Nonhomogeneous Boundary Condition

A vertical circular cylinder which is in periodic oscillatory motion with small amplitudes in finite depth is considered. The usual assumptions necessary for the potential flow stand valid in the present study. A classical perturbation procedure is employed to solve the nonlinear problem through the second-order. According to the solution method presented, the fluid domain is separated into interior and exterior regions in which boundary-value problems (BVP) are decomposed into two BVPs each having one nonhomogeneous boundary condition. A nonhomogeneous second-order free-surface condition is treated by means of a modified form of Weber's integral theorem. Eigenfunction expansions are used for homogeneous solutions. Thus, to conclude the solution, the exterior and interior solutions are then matched on the common boundary. Numerical results are given for a heaving vertical circular cylinder. Wave field analysis around a vertical cylinder shows that the second-order wave pattern is typically dominated by the second-order wave number related to the second-order dispersion relation. The procedure also satisfies the conditions at infinity through the second-order.

scholarly journals Boussinesq Model and CFD Simulations of Non-Linear Wave Diffraction by a Floating Vertical Cylinder

2020 ◽  
Vol 8 (8) ◽  
pp. 575
Author(s):  
Sarat Chandra Mohapatra ◽  
Hafizul Islam ◽  
C. Guedes Soares
Keyword(s):  
Wave Diffraction ◽  
Perturbation Technique ◽  
Harmonic Wave ◽  
Vertical Cylinder ◽  
Numerical Data ◽  
Second Order ◽  
Wave Number ◽  
Linear Wave ◽  
Cfd Simulations ◽  
Boussinesq Model

A mathematical model for the problem of wave diffraction by a floating fixed truncated vertical cylinder is formulated based on Boussinesq equations (BEs). Using Bessel functions in the velocity potentials, the mathematical problem is solved for second-order wave amplitudes by applying a perturbation technique and matching conditions. On the other hand, computational fluid dynamics (CFD) simulation results of normalized free surface elevations and wave heights are compared against experimental fluid data (EFD) and numerical data available in the literature. In order to check the fidelity and accuracy of the Boussinesq model (BM), the results of the second-order super-harmonic wave amplitude around the vertical cylinder are compared with CFD results. The comparison shows a good level of agreement between Boussinesq, CFD, EFD, and numerical data. In addition, wave forces and moments acting on the cylinder and the pressure distribution around the vertical cylinder are analyzed from CFD simulations. Based on analytical solutions, the effects of radius, wave number, water depth, and depth parameters at specific elevations on the second-order sub-harmonic wave amplitudes are analyzed.

scholarly journals Hydrodynamic Forces on a Submerged Circular Cylinder in Two-layer Fluid with an Ice-cover

2021 ◽  
Vol 23 (08) ◽  
pp. 282-294
Author(s):  
Manomita Sahu ◽  
◽  
Dilip Das ◽  
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Flexural Rigidity ◽  
Lower Layer ◽  
Wave Theory ◽  
Finite Depth ◽  
Ice Cover ◽  
Hydrodynamic Forces ◽  
Wave Number ◽  
Infinite Layer

We consider problems based on linear water wave theory concerning the interaction of wave with horizontal circular cylinder submerged in two-layer ocean consisting of a upper layer of finite depth bounded above by an ice-cover and below by an infinite layer of fluid of greater density, the ice-cover being modelled as an elastic plate of very small thickness. Using the method of multipoles, we formulate the problems of hydrodynamic forces on a submerged cylinder in either the upper or the lower layer. The vertical and horizontal forces on the circular cylinder are obtained and depicted graphically against the wave number for various values of flexural rigidity of ice-cover to show the effect of the presence of ice-cover on these quantities. Also when the flexural rigidity and surface density of the ice-cover are taken to be zero, the ice-cover tends to a free-surface. Then all the forces are the same as in the case of two-layer fluid with free surface.

Time-Domain Second-Order Wave Radiation in Two Dimensions

1993 ◽  
Vol 37 (01) ◽  
pp. 25-33 ◽  
Author(s):  
Michael Isaacson ◽  
Joseph Y. T. Ng
Keyword(s):  
Circular Cylinder ◽  
Time Domain ◽  
Body Position ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Second Order ◽  
The Body ◽  
Wave Radiation ◽  
Surface Boundary ◽  
Time Step

This paper presents a time-domain second-order method to study the nonlinear wave radiation problem in two dimensions. A time-stepping scheme is adopted to obtain the resulting flow development which satisfies the nonlinear free-surface boundary conditions and the radiation condition to second order, and the numerical procedure utilizes a boundary integral equation method based on Green's theorem to calculate the field solution at each time step. The body surface boundary condition is expanded about the mean body position to second order by a Taylor series. The method is applied to the cases of a semi-submerged circular cylinder and a rectangular cylinder undergoing sinusoidal sway, heave and roll motions. For the case of the circular cylinder, comparisons of the computed hydrodynamic forces at first and second order are made with previous theoretical and experimental results and a favorable agreement is indicated. The importance of second-order effects in the calculation of the hydrodynamic force is discussed.

Numerical Simulation of Nonlinear Wave Diffraction by a Vertical Cylinder

1992 ◽  
Vol 114 (1) ◽  
pp. 36-44 ◽  
Author(s):  
C. Yang ◽  
R. C. Ertekin
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Radiation Condition ◽  
Wave Force ◽  
Second Order ◽  
Time Stepping

A three-dimensional time domain approach is used to study nonlinear wave diffraction by a fixed, vertical circular-cylinder that extends to the sea floor. In this approach, the development of the flow can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any instant of time is obtained by the boundary-element method. In the numerical calculations, the exact body-boundary condition is satisfied on the instantaneous wetted surface of the cylinder, and an extended Sommerfeld condition is developed and used as the numerical radiation condition. The fourth-order Adams-Bashford method is employed in the time stepping scheme. Calculations are done to obtain the nonlinear diffraction of solitary waves and Stokes second-order waves by a vertical circular-cylinder. Numerical results are compared with the available linear and second-order wave-force predictions for some given wave height and wavelength conditions, and also with experimental data. Present horizontal force results agree better with the experimental data than the previous predictions.

scholarly journals WAVE-INDUCED SEEPAGE EFFECTS ON A VERTICAL CYLINDER

1980 ◽  
Vol 1 (17) ◽  
pp. 108
Author(s):  
Thomas J.P. Durand ◽  
Peter L. Monkmeyer
Keyword(s):  
Circular Cylinder ◽  
Water Waves ◽  
Theoretical Calculations ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Pressure Amplitude ◽  
Uplift Force ◽  
Overturning Moment ◽  
Wave Induced ◽  
Circular Base

This study deals with the seepage effects experienced by a large, vertical, circular cylinder resting on a submerged bed of sand when planar water waves interact with it. Potential theory is used to describe the seepage flow field. The sea bottom pressure condition is determined from the water field velocity potential derived by MacCamy and Fuchs (1954) in the case of planar waves diffracted by a large impervious cylinder. Consideration is also given to cylinders with a thin circular base whose diameter exceeds that of the cylinder itself. The problem formulation as well as the initiation of the analysis apply to the general case of a bed of sand with finite depth. For the case of infinite depth of the porous medium, theoretical solutions for the seepage pressure are obtained in the form of infinite integrals. Theoretical solutions for the pressure along the cylinder circular base are then derived, leading by integration to closed form expressions for the wave-induced seepage uplift force and overturning moment exerted on the cylinder. These expressions for the force and moment, which are presented in non-dimensional form are shown to be universal functions of a unique variable. Graphs are provided so that very few computations are required to determine the uplift force and overturning moment exerted on a cylinder. A comparison with various approximate theories reveals the present theory to be the only one which gives reliable results in general. The amplitude and phase angle of the oscillating wave-induced pressure along the cylinder base are determined numerically. Results for the pressure amplitude are presented as non-dimensional ratios to the amplitude of the pressure that would prevail if no cylinder were disturbing the wave field. Expressions for the exit gradient around the cylinder base are also determined. Contours of the ratio of the exit gradient to the one that would prevail in the absence of a cylinder are presented. Laboratory measurements of uplift pressure amplitudes on a circular cylinder show good agreement with theoretical calculations.

Sound and Electromagnetic Wave Scattering by a Compact Circular Pore With a Finite Depth

2009 ◽  
Author(s):  
Chih-Yu Kuo ◽  
Ruey-Lin Chern ◽  
Chien-Cheng Change
Keyword(s):  
Electromagnetic Wave ◽  
Wave Scattering ◽  
Finite Depth ◽  
Higher Order ◽  
Wave Number ◽  
Wave Radiation ◽  
Matched Asymptotic Expansion ◽  
Wave System ◽  
Electromagnetic Wave Scattering ◽  
Inner Region

The three dimensional wave scattering of an oblique wave incident on a flanged circular compact pore of finite depth is solved analytically by the method of matched asymptotic expansion. We assume smallness of the product of the incident wave number and the pore radius and divide the scattering field into an inner region and an outer radiation region. For the wave system, the physical variables, e.g. sound pressure, electric/magnetic fields, satisfy the Laplace equation in the inner region. For the circular shaped pores, they can be solved by the method developed by Fabrikant. Then via the matching processes, the wave radiation in the outer field is determined. The theory is developed first for sound wave scattering. Both rigid and pressure-release boundary conditions are investigated. For a pore with a finite depth, the leading radiation terms for both conditions are at the same order of magnitude. They contain one monopole and one dipole for the former and one dipole for the latter. Quadrupoles and an octupole are found in the next higher order. Subsequently, the theory is applied to the electromagnetic wave scattering. The problems are formulated based on the duality property of the source-free Maxwell equations. A multipole expansion for the scattering wave similar to the acoustic counterpart is obtained. A few residue multipoles arising from the higher order inner region are found. The leading dipoles and their orientation are demonstrated.

scholarly journals NONLINEAR DIFFRACTION BY A VERTICAL CYLINDER

1988 ◽  
Vol 1 (21) ◽  
pp. 1
Author(s):  
David L. Kriebel
Keyword(s):  
Vertical Cylinder ◽  
Wave Structure ◽  
Finite Depth ◽  
Second Order ◽  
Wave Crest ◽  
Wave Runup ◽  
Nonlinear Diffraction ◽  
Stokes Waves ◽  
Dynamic Quantity ◽  
Wave Region

A theoretical solution is developed for the interaction of second-order Stokes waves with a large vertical circular cylinder in water of finite depth. The solution is obtained in terms of the velocity potential such that any kinematic or dynamic quantity of interest may be derived, consistent to the second perturbation order. In this study, the second-order wave field around the cylinder is determined, showing the modification of the incident Stokes waves by wave-wave and wave-structure interactions, both in the reflection-dominated up-wave region and in the diffraction-dominated down-wave region. The theory is then compared to experimental data for wave runup and rundown amplitudes on the cylinder as well as for wave crest and trough envelopes in the up-wave and down-wave regions.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

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