scholarly journals An Analytical Solution for the Interaction of Waves with Arrays of Circular Cylinders

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhao Mi ◽  
Long Pengzhen ◽  
Wang Piguang ◽  
Zhang Chao ◽  
Du Xiuli
Keyword(s):  
Analytical Solution ◽  
Multiple Scattering ◽  
Incident Wave ◽  
Scattering Problem ◽  
Scattered Wave ◽  
Wave Force ◽  
Circular Cylinders ◽  
Wave Forces ◽  
Incident Waves ◽  
Variable Separation Method

This paper presents an analytical method to investigate the multiple scattering problem within arrays of vertical bottom-mounted circular cylinders subjected to linear incident waves. Based on the Laplace equation and boundary conditions on the seabed and surface, a formulation of a two-dimensional multiple scattering problem is first obtained by using the variable separation method. Furthermore, the analytical solution of the wave forces on multiple circular cylinders is derived, which consists of the incident wave force due to the linear incident wave and the scattered wave forces considering multiple scattering waves. The presented analytical solution is validated by comparing its results with a numerical method, and the result shows that the analytical solution is in good agreement with the numerical one. Finally, the multiple scattering analysis is conducted on arrays of cylinders with different incident wave numbers, distances between cylinders, and quantities.

DISPERSION OF WAVE FORCES ON CAISSON BREAKWATERS USING INTERLOCKING SYSTEMS

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Jihye Seo ◽  
Jin-Hak Yi ◽  
Deock-Hee Won ◽  
Woo-Sun Park
Keyword(s):  
Incident Wave ◽  
Numerical Experiments ◽  
Wave Dispersion ◽  
Wave Force ◽  
Normal Direction ◽  
Wave Forces ◽  
Dispersion Characteristics ◽  
Dispersion Effect ◽  
The Stability

Interlocking caisson-type breakwaters have recently gained attention for enhancing the stability of the conventional breakwaters. In this study, the dispersion characteristics of wave forces using interlocking systems connecting the upper part of caissons with cables in the normal direction of breakwaters were investigated. Based upon numerical experiments, the higher wave forces are transmitted through the cable as the angle of incident wave increases, while the maximum allowable wave force was capable of being increased by sharing the wave forces with the adjacent caissons. It was also found that the larger the stiffness of the interlocking cable, the larger the wave-dispersion effect.

scholarly journals Horizontal Forces Due to Waves Acting on Large Vertical Cylinders in Deep Water

1972 ◽  
Vol 94 (4) ◽  
pp. 862-866
Author(s):  
E. R. Johnson
Keyword(s):  
Deep Water ◽  
Large Diameter ◽  
Wave Force ◽  
Circular Cylinders ◽  
Wave Forces ◽  
Typical Application ◽  
Model Studies ◽  
Horizontal Wave ◽  
Horizontal Wave Force ◽  
Vertical Cylinders

The special case of horizontal wave forces on large vertical cylinders in deep water is considered. The typical application for such a case is the calculation of horizontal forces on column stabilized floating ocean platforms. Existing literature discussing horizontal wave forces on cylinders does not generally agree on how to predict these forces. Since for large diameter cylinders in deep water the maximum force is completely inertial, the problem of deriving a solution is considerably simplified. In this study, an expression for the maximum horizontal wave force on large diameter circular cylinders mounted vertically in deep water has been analytically derived. Experimental model studies were also conducted and the resulting measured forces were within 20 percent of predicted forces. An example of how to predict horizontal wave forces using the methods of this report is given.

Application of a Hybrid Boussinesq-Panel Model for Motion Predictions of a Moored Sevan-Floater in Finite Water Depth

2017 ◽  
Author(s):  
Jikun You ◽  
Einar Bernt Glomnes
Keyword(s):  
Water Depth ◽  
Low Frequency ◽  
Boussinesq Equations ◽  
Wave Force ◽  
Irregular Waves ◽  
Wave Forces ◽  
Rankine Source ◽  
Panel Model ◽  
Finite Water Depth ◽  
Incident Waves

This paper presents the applications of an efficient hybrid time-domain simulation model for predicting moored Sevan-floater motions in irregular waves and finite water depth. The irregular incident waves are modeled by the extended Boussinesq equations, which can capture wave-wave interactions and the low-frequency long waves accurately in finite and shallow water depth. By imposing the incident wave kinematics on the surface of the floater, a panel model based on Rankine source method is applied for the calculation of wave forces and corresponding floater motions. The contributions from low-frequency components in incident waves as well as their diffraction effects are included in the wave force calculations. Validation of the irregular waves simulated by the present numerical model are performed against experimental data. Then, the simulated moored floater motions are compared with model test results and results based on Newman’s approximation. The general good agreements with experimental results demonstrate the present model can be used as an alternative for this problem while Newman’s approximation shows non-conservative results.

scholarly journals Numerical Simulation of Breaking Wave Loading on Standing Circular Cylinders with Different Transverse Inclined Angles

2020 ◽  
Vol 10 (4) ◽  
pp. 1347
Author(s):  
Sen Qu ◽  
Shengnan Liu ◽  
Muk Chen Ong ◽  
Shuzheng Sun ◽  
Huilong Ren
Keyword(s):  
Experimental Data ◽  
Vertical Cylinder ◽  
Wave Force ◽  
High Order ◽  
Numerical Results ◽  
Circular Cylinders ◽  
Wave Forces ◽  
Breaking Wave ◽  
Time Step ◽  
Inclined Angle

The purpose of this paper is to numerically simulate the breaking wave past a standing cylinder with different transverse inclined angles. The numerical simulations are carried out by solving the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations with the k − ω S S T turbulence model. The air–water interface is captured using the Volume of Fluid (VOF) method. The convergence studies on the grid and time-step are performed by examining the total horizontal breaking wave forces on the vertical cylinder. The present numerical results have been validated with the published experimental data. A good agreement is obtained between the present numerical results and the experimental data in terms of the surface elevation and the horizontal breaking wave force. Moreover, the total horizontal breaking wave force is decomposed into low-order and high-order wave forces through Fast Fourier Transform (FFT). It is observed that the free surface elevations in front of the cylinder and the normalized high-order wave force have a minimum value when the transverse inclined angle of the cylinder is 45°. The secondary load causing the higher-harmonic ringing motion of structures is not observed when the cylinder is placed with the transverse inclined angles of 30° and 45°.

Interaction of water waves with three-dimensional periodic topography

2001 ◽  
Vol 434 ◽  
pp. 301-335 ◽  
Author(s):  
R. PORTER ◽  
D. PORTER
Keyword(s):  
Incident Wave ◽  
Water Waves ◽  
Homogeneous Problem ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Trapped Waves ◽  
Trapped Mode ◽  
Bed Elevation ◽  
Input Mode ◽  
Incident Waves

The scattering and trapping of water waves by three-dimensional submerged topography, infinite and periodic in one horizontal coordinate and of finite extent in the other, is considered under the assumptions of linearized theory. The mild-slope approximation is used to reduce the governing boundary value problem to one involving a form of the Helmholtz equation in which the coefficient depends on the topography and is therefore spatially varying.Two problems are considered: the scattering by the topography of parallel-crested obliquely incident waves and the propagation of trapping modes along the periodic topography. Both problems are formulated in terms of ‘domain’ integral equations which are solved numerically.Trapped waves are found to exist over any periodic topography which is ‘sufficiently’ elevated above the unperturbed bed level. In particular, every periodic topography wholly elevated above that level supports trapped waves. Fundamental differences are shown to exist between these trapped waves and the analogous Rayleigh–Bloch waves which exist on periodic gratings in acoustic theory.Results computed for the scattering problem show that, remarkably, there exist zeros of transmission at discrete wavenumbers for any periodic bed elevation and for all incident wave angles. One implication of this property is that total reflection of an incident wave of a particular frequency will occur in a channel with a single symmetric elevation on the bed. The zeros of transmission in the scattering problem are shown to be related to the presence of a ‘nearly trapped’ mode in the corresponding homogeneous problem.The scattering of waves by multiple rows of periodic topography is also considered and it is shown how Bragg resonance – well-established in scattering of waves by two-dimensional ripple beds – occurs in modes other than the input mode.

Radiation and scattering of water waves by rigid bodies

1971 ◽  
Vol 46 (1) ◽  
pp. 151-164 ◽  
Author(s):  
J. L. Black ◽  
C. C. Mei ◽  
M. C. G. Bray
Keyword(s):  
Surface Waves ◽  
Incident Wave ◽  
Water Waves ◽  
Variational Formulation ◽  
Rigid Bodies ◽  
Small Oscillation ◽  
Circular Cylinders ◽  
Wave Forces ◽  
Far Field ◽  
Plane Incident Wave

Schwinger's variational formulation is applied to the radiation of surface waves due to small oscillation of bodies. By means of Haskind's theorem the wave forces on a stationary body due to a plane incident wave are found using only far-field properties. Results for horizontal rectangular and vertical circular cylinders are presented.

scholarly journals WAVE FORCE ON A VESSEL TIED AT OFFSHORE DOLPHINS

1972 ◽  
Vol 1 (13) ◽  
pp. 92
Author(s):  
Yoshimi Goda ◽  
Tomotsuka Yoshimura
Keyword(s):  
Wave Scattering ◽  
Maximum Amplitude ◽  
Wave Force ◽  
Elliptical Cylinder ◽  
Wave Forces ◽  
Reference Volume ◽  
Wave Approach ◽  
Directional Wave ◽  
The One ◽  
Incident Waves

The solution of wave scattering by a vertical elliptical cylinder is applied to calculate the wave forces exerted upon it. The wave forces in the directions of long and short axes of ellipsis are shown in nondimensional forms as the functions of the angle of wave approach, the diameter-to-wavelength ratio, and the aspect ratio of ellipsis. The results of wave force computed are also shown in terms of the virtual mass coefficients associated with the reference volume of the circular cylinder the diameter of which is approximately equal to the apparent width of the elliptical cylinder observed from the direction of wave approach. Theory is further applied for the wave forces acting upon a vessel moored tight at offshore dolphins and the forces transmitted to the dolphins through the vessel. The vessel is approximated with the fixed elliptical cylinder having the same width-to-length ratio. The computation with directional wave spectra shows that a tanker of 200,000 D.W.T. may exert the force of about 1,400 tons at the one-third maximum amplitude to each breasting dolphin when the tanker is exposed to the incident waves of H,/„=1.0m and T» / =10 sec from the broadside.

scholarly journals Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction

2021 ◽  
Vol 33 (6) ◽  
pp. 275-286
Author(s):  
Jae-Sang Jung ◽  
Changhoon Lee
Keyword(s):  
Standing Waves ◽  
Wave Theory ◽  
Wave Force ◽  
Wave Forces ◽  
Linear Wave ◽  
Random Waves ◽  
Linear Wave Theory ◽  
Incident Wave Angle ◽  
Wave Angle ◽  
Incident Waves

In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.

scholarly journals NONLINEAR METHOD FOR REAL-TIME WAVE FORCE RECONSTRUCTION ON A CYLINDER BY USING MEASURED WAVE ELEVATION

2020 ◽  
pp. 6
Author(s):  
Jiabin Liu ◽  
Anxin Guo
Keyword(s):  
Circular Cylinder ◽  
Real Time ◽  
Linear Method ◽  
Wave Force ◽  
Wave Forces ◽  
Frequency Wave ◽  
Wave Fields ◽  
Wave Elevation ◽  
Force Reconstruction ◽  
Incident Waves

For a constructed offshore structure, wave force evaluation on its foundation in an intricate wave field will benefit the load data collection and structural safety monitoring. Then, the collected data can provide valuable references for similar structures constructed in the same ocean region in the future. A real-time wave force prediction can further contribute to the active control of the structural dynamic responses. According to the incident waves known or unknown, the wave force reconstruction issue can be divided into two categories. When the incident waves are known, the wave forces on the cylinder can be achieved by the theoretical methods or numerical methods. When the incident waves are unknown, researchers try to reconstruct the wave force indirectly. For a small-scale cylinder, researchers predicted the wave forces by using the Morison equation in random wave fields with measured data of wave elevation. These studies indicated a shortcut for determining the wave force on the cylinder by using the data of water surface elevation. However, the wave fields are assumed to be undisturbed by the structure in the mentioned studies. For a vertical larger-scale cylinder, Liu et al. (2018) established a prediction method to reconstruct wave force by using the recorded data of wave elevation around the cylinder. A linear method for the circular cylinder is provided that shows an excellent reconstruction of wave force for its dominant frequent components. However, reconstruction results showed that high frequency wave forces are underestimated and low frequency wave forces are overestimated, which means the linear method is incapable to predict the nonlinear wave forces on the structure. An improved method is built for reconstructing wave forces on a circular cylinder in the real-time. Two different algorithms, Fast Fourier Translation (FFT) and Recursive Least Squares (RLS), for real-time reconstruction are conducted. The present method can be applied for the data collection of wave loads on a constructed offshore structure.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/PYOuCNP8pgQ

The Concept of the Optimum Alignment of Discharge Pipelines Due to the Minimization of the Wave Forces

1992 ◽  
Vol 25 (9) ◽  
pp. 211-216
Author(s):  
A. Akyarli ◽  
Y. Arisoy
Keyword(s):  
Wave Height ◽  
Wave Force ◽  
Wave Forces ◽  
Wave Direction ◽  
Incoming Wave ◽  
Pipeline Route ◽  
Optimum Alignment ◽  
The Cost ◽  
Resultant Wave

As the wave forces are the function of the wave height, period and the angle between the incoming wave direction and the axis of the discharge pipeline, the resultant wave force is directly related to the alignment of the pipeline. In this paper, a method is explained to determine an optimum pipeline route for which the resultant wave force becomes minimum and hence, the cost of the constructive measures may decrease. Also, the application of this method is submitted through a case study.

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