Wave forces acting on a submerged horizontal circular cylinder in oblique waves and on a vertical cylinder in deep waves

This paper presents a method of estimating wave forces acting on a submerged horizontal circular cylinder fixed in oblique waves.The experiments show that drag and inertia coefficients in beam sea are available for calculating the wave forces in oblique waves.Wave forces exerted on a vertical circular cylinder in deep waves are also investigated.The experimental results show that wave forces acting on the vertical cylinder coincide approximately with hydrodynamic forces acting on a submerged circular cylinder in an oscillating fluid.     

Comparison of flow patterns in the near wake of a circular cylinder and a square cylinder placed near a plane wall

The flow patterns in the near wake of a cylinder (either circular or square in shape, D=25 mm) placed in the proximity of a fully developed turbulent boundary layer (thickness δ=0.4D) are investigated experimentally using particle image velocimetry (PIV). The effects of changing the gap height (S) between the cylinder bottom and the wall surface, over the gap ratio range S/D=0.1–1.0, have been investigated. The results show that both the ensemble-averaged and instantaneous flow fields are strongly dependent on S/D. The flow patterns for the two types of cylinders share many similarities with respect to the change in S/D, such as the reduced recirculation length and increased velocity fluctuation in the near wake with increasing S/D, as well as the trend of suppression of vortex shedding at small S/D and onset of vortex shedding at large S/D. However, developments of the shear layers, in terms of wake width, flow curvature, etc., are considerably different for these two types of cylinders. In general, the wake development and momentum exchange for the square cylinder are slower those for the circular cylinder at the same gap ratio. Correspondingly, it is shown that the periodic vortex shedding is delayed and weakened in the case of square cylinder, as compared to that of the circular cylinder at the same S/D.     

Computations of forces on, and particle orbits around, horizontal cylinders under steep waves

A numerical method, based on a boundary integral equation combined with a non-linear time stepping procedure for the free water surface, is developed for simulations of the interaction between highly non-linear water waves and submerged horizontal cylinders. The method is based on potential theory, and the omission of viscous effects restricts the wave-structure interaction computations to low Keulegan-Carpenter numbers where inertia forces are dominant. The numerical scheme is verified by computations with a steep wave of exact form during several wave periods, and by computations of a breaking wave. A new method for tracing the orbits of water particles in the fluid domain is developed, and the influence from submerged structures on the orbits is visualized through several computational examples. The wave forces on submerged structures are computed and are found to correspond well with other computed results for low Keulegan-Carpenter numbers.     

Pressures and forces on inclined cylinders due to regular waves

The variation of the dynamic pressures around a circular cylinder due to regular waves is studied in a wave basin of constant water depth of 3 m. The measuring segment consisted of 12 pressure transducers placed at an elevation of 0.8 m below the still water level. The tests were conducted with the cylinder axis inclined with respect to the vertical plane along and against wave direction. The results on the variation of dimensionless pressures with the non-dimensional input wave parameters are reported for different angles of orientation of the cylinder. The sectional normal force obtained by integrating the pressures is also presented as a function of wave steepness and the effect of angle of orientation of the cylinder is also reported.     

Radiation and scattering of surface waves by a group of submerged,horizontal, circular cylinders

One of the major methods available for investigating the interaction of water waves with arbitrarily shaped structures is based on the classical theory of Green's functions. For multiple bodies, however, this technique can become expensive in terms of both computer storage and execution time and it is desirable for special geometrics where possible, to seek simpler methods. In this paper, the radiation and scattering of surface waves by a group of parallel, horizontal, circular cylinders, submerged in deep water is studied using a method involving multipole potentials. The method is developed for any number of submerged, parallel, horizontal cylinders with arbitrary positions and radii. In particular, hydrodynamic coefficients are determined for various configurations of two and three cylinders and a comparison is made with results obtained for a cylinder in isolation.     

Statistics of wave forces on large horizontal cylinders

To the first order in a Stokes expansion, the pressure force exerted by a sea state on a large horizontal cylinder represents a stationary random Gaussian process. A relationship is obtained between the spectrum of this process and the wave spectrum. As a consequence, the basic statistical properties of the height and period of the individual waves of the force-process are also obtained. It is proven that these statistical properties agree very well with the data from a small scale field experiment.     

Forces on a circular cylinder near a plane wall

The drag and lift force are measured on circular cylinders fitted with end plates in a wind tunnel. The gap between the cylinder and the wall, G, the thickness of the turbulent boundary layer along the wall, δ, and the Reynolds number, Re, are varied in the following ranges: 0 < G/D < 2, 0.12 < δ/D < 0.97 and 4.8 × 10⁴ Re 3 × 10⁵. The lift and drag coefficients are presented in terms of a new variable G/δ.

It is found that the lift coefficient is governed by the gap to diameter ratio G/D while the drag coefficient is dominated by the ratio of gap to thickness of the boundary layer, G/δ.     

Second-order vertical and horizontal wave forces on a circular dock

A second-order potential solution is presented for the diffraction of a nonlinear progressive wave in finite-depth water, incident on a fixed circular dock. The usual perturbation analysis is used to produce first- and second-order subproblems. The mathematical method is based on the assumption that inner and outer solutions exist and these are matched by the requirements of continuity for mass flux and pressure between adjacent regions. It is shown that the solutions for the second-order problem can be derived in the same manner as in the first-order theory.     

Wave forces on submarine pipelines near a plane boundary

Forces induced by regular waves on submarine pipelines resting on as well as near a plane boundary and aligned parallel to wave fronts of the oncoming waves are investigated experimentally. The inline hydrodynamic coefficients of drag and inertia are evaluated through the use of Morison equation and the least squares method. The transverse force is analysed in terms of maximum transverse force and transverse root mean square (r.m.s.) coefficients. The resulting inline and transverse hydrodynamic coefficients are correlated with the period parameter or Keulegan-Carpenter number and relative clearance of the pipeline from the plane boundary. The effect of depth parameter on these coefficients and the correlation between maximum transverse force and transverse r.m.s. coefficients are also reported.     

平面波与圆柱群的相互作用分析

简要分析了水波与圆柱群的相互作用问题。导入柱间的相位关系,改进了文献[2]中的公式,并且证明在柱间互不连接条件下,解是存在的。数值结果与文献[2]的分析解以及文献[6]的数值解和实验数据有很好的一致性。     

透空式水平板波浪上托力计算方法

在透空式平板波浪上托力试验研究基础上,针对实际工程应用要求,提出相对简便的透空式平板下波浪局部上托力和最大总上托力计算方法,包括上托力大小、分布宽度和发生位置。对具体工程实例的计算结果表明,该方法与实验值有着较好的一致性。     

Incipient motion on a horizontal granular bed in non-breaking water waves

A criterion for initiation of sediment movement on a horizontal bed under non-breaking waves is established. Bagnold's sediment transport model is used. The dissipation rate of energy has been related to the length and velocity scales of the large-scale turbulence. The proposed equation is compared with the available laboratory results for fine and coarse material 0.1 mm < D ? 45 mm over a wide range of particle sizes, density ratios and liquid viscosities and a reasonable agreement between the two is obtained. An incipient motion hypothesis based on the development of vorticity is proposed.     

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.     

近壁圆柱绕流水动力特性数值模拟与实验研究

通过数值模拟和物理模型实验,对距壁面一定高度的圆柱绕流水动力特性进行了研究。数值模拟采用有限体积法对标准k-ε模式方程进行离散,采用SIMPLE算法进行求解,模拟绕流流场。在物理模型实验中,将PVC圆管制作的实验模型安放在水槽内,在圆管的跨中沿表面周向均匀布置水下压力传感器,用于测量绕流圆柱体表面动水压力分布。通过改变Re数和间隙比来分析它们对近壁圆柱绕流水动力特性的影响。基于数值流动显示技术,给出了近壁绕流流场的尾流流态分析。通过数值结果与实验结果的对比,对近壁绕流圆柱体的升力系数及其表面动水压力分布进行了研究,对比结果显示了较好的一致性。     

Interaction of regular waves with a group of dual porous circular cylinders

Diffraction of linear waves around a group of dual porous cylinders consisting of a thin and porous outer cylinder with an impermeable inner cylinder is investigated analytically based on the eigenfunction expansion method proposed by Spring and Monkmeyer [Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. In: Proceedings 14th international coastal engineering conference. 1974. p. 1828–47] and further modified by Linton and Evans [Linton CM, Evans DV. The interaction of waves with arrays of vertical circular cylinders. Journal of Fluid Mechanics 1990;215:549–69]. The present formulation is an extension of the work of Wang and Ren [Wang KH, Ren X. Wave interaction with a concentric porous cylinder system. Ocean Engineering 1994;21(4):343–60], wherein; the interaction of linear waves with a single concentric porous cylinder system was studied. This paper aims at investigating the influence of multiple interactions between the cylinders in the group on the hydrodynamic wave forces, wave run-up and free-surface elevation in their vicinity. Further, the study focuses on the variation of the forces and run-up on the individual cylinders within the group compared to that on isolated cylinders.     

透空式水平板波浪总上托力试验研究

通过系列模型试验,对透空水平板下波浪总上托力进行了研究,结果表明：平板下最大总上托力并不与最大冲击压强同步发生。为此,依据试验结果对波浪总上托力产生机理和影响因素进行详细分析,提出透空水平板波浪最大总上托力的计算公式,试验结果表明,该公式与实验值有着较好的一致性。     

Interaction between waves and an array of floating porous circular cylinders

The present study theoretically as well as experimentally investigates the interaction between waves and an array of porous circular cylinders with or without an inner porous plate based on the linear wave theory.To design more effective floating breakwaters,the transmission rate of waves propagating through the array is evaluated.Each cylinder in the array is partly made of porous materials.Specifically,it possesses a porous sidewall and an impermeable bottom.In addition,an inner porous plate is horizontally fixed inside the cylinders.It dissipates the wave more effectively and eliminates the sloshing phenomenon.The approach suggested by Kagemoto and Yue(1986) is adopted to solve the multiple-scatter problem,while a hierarchical interaction theory is adopted to deal with hydrodynamic interactions among a great number of bodies,which efficiently saves computation time.Meanwhile,a series of model tests with an array of porous cylinders is performed in a wave basin to validate the theoretical work and the calculated results.The draft of the cylinders,the location of the inner porous plate,and the spacing between adjacent cylinders are also adjusted to investigate their effects on wave dissipation.     

圆形数值波浪水池斜向和多向入射波浪模拟研究

为了研究斜向入射波浪,基于三维不可压缩两相流模型,开发了一套圆形数值波浪水池数值模型。在圆形波浪水池中,通过源项造波法成功生成了任意入射方向的波浪,并且利用人工摩擦项模拟阻尼区以数值耗散反射波浪。模型基于嵌入式多块网格体系,采用FVM法(finite volume method)离散Navier-Stokes方程,VOF法(volume of fluid)追踪自由水面。试验结果表明,斜向入射波浪的模拟结果与理论值基本一致,圆形波浪水池在模拟斜向入射波浪时,有效区域的面积较传统波浪水池显著增大,而且有效区域受波浪入射角度的影响也较小。同时,通过叠加多列斜向入射波浪,模拟出了多向交叉波列,并通过与理论结果对比,发现其具有较高的精度。     

Total horizontal and vertical forces of irregular waves on partially perforated caisson breakwaters

In this study, the total horizontal and vertical forces as well as the phase differences of irregular waves on a partially perforated caisson breakwater are investigated. The partially perforated caisson is located on a rubble fill foundation and filled with rock. Based on linear potential theory, a simple semi-analytical solution of the present problem is developed by means of the matched eigenfunction method and the finite element method. Experimental tests are also conducted to validate the theoretical model and examine the wave forces acting on the perforated caisson. The effects of some of the main factors on the total wave forces and the phase difference are examined. Theoretical and experimental studies show that when the total horizontal force reaches its peak, the simultaneous total vertical (upward) force is rather small or even becomes downwards. This is due to the existence of an obvious phase difference between the time histories of the total horizontal and vertical forces, which is an important advantage of perforated caissons over traditional structures.     

The effect of frequency dispersion on plane waves generated as a result of bed motions

Using a linear statement, the paper studies surface waves occurring due to minor shifts of the bottom sections. A plane case is considered. An analytical solution to the problem has been derived using Fourier transforms. Asymptotic laws for the degeneration of waves propagating over finite bottom deformations have been defined. Numerical analysis of the integrals is applied to study the effect of the horizontal extent of a wave generation area and bottom irregularities on the shape of waves and their amplitudinal and energetic parameters. Attention is focused on the manifestation of frequency dispersion at the stage of wave generation as a developed wave process. Translated by Vladimir A. Puchkin.