A numerical study of three-dimensional wave interaction with a square cylinder

In this study, a three-dimensional numerical model is used to study the wave interaction with a vertical rectangular pile. The model employs the large eddy simulation (LES) method to model the effect of small-scale turbulence. The velocity and vorticity fields around the pile are presented and discussed. The drag and inertial coefficients are calculated based on the numerical computation. The calculated coefficients are found to be in a reasonable range compared with the experimental data. Additional analyses are performed to assess the relative importance of drag and initial effects, which could be quantified by the force-related Keulegan and Carpenter (KC) number: KC_f=UT/(4πL). Here U is the maximum fluid particle velocity, T the wave period and L the length of structure aligned with the wave propagation direction. For small KC_f, the effective drag coefficient is proportional to 1/KC_f, provided the wavelength is much longer than the structural length. When wavelength is comparable to the structure dimension, the effective drag coefficient would be reduced significantly due the cancellation of forces, which has been demonstrated by numerical results.     

Significance of relative velocity in the estimation of drag force of a tethered spherical float

In the present study, a tethered spherical float undergoing oscillatory motion in regular waves is analysed. Float velocity is computed through dynamical equation of motion and particle velocity using linear wave theory. The results show that variation of particle velocity with respect to wave period, wave height or water depth is small compared to the variation of float velocity with respect to the same parameters. The results further indicate that the difference between float velocity and particle velocity is considerable and, in such cases, the relative velocity instead of the particle velocity has to be considered for drag force or drag power estimation. However, it is suggested that float velocity must be higher than the particle velocity in order to use relative velocity in drag force or drag power estimation.     

Dynamic Response Analysis of Risers Subjected to Combined Wave and Current Loading

A dynamic response analysis in the frequency domain is presented for risers subjected to combined wave and current loading. Considering the effects of current, a modified wave spectrum is adopted to compute the linearized drag force. An additional drag force convolution term is added to the linearized drag force spectrum, therefore the error is reduced which arises from the truncation of higher order terms in the drag force auto-correlation function. An expression of linearized drag force spectrum is given taking the relative velocity into account. It is found that the additional term is a fold convolution integral. In this paper dynamic responses of risers are investigated, while the influence of floater motion on risers is considered. The results demonstrate that the accuracy of the present method reaches the degree required in time domain analysis.     

In-line force on a cylinder translating in oscillatory flow

Experiments were conducted with smooth and sand-roughened cylinders moving with constant velocity in a sinusoidally oscillating flow to determine the drag and inertia coefficients and to examine the effect of wake biasing on the modified Morison equation. The various flow parameters such as the relative cylinder velocity. Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for both smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag-inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and current induced loads on circular cylinders.     

动波浪壁圆柱绕流三维数值模拟

利用计算流体力学软件Fluent开展了三维动波浪壁圆柱绕流的数值模拟,建立了三维运动波浪壁圆柱模型,通过C语言自编程序实现波浪壁面的运动控制,并保证壁面变形时网格的高质量。在来流速度u=0.125 m/s、雷诺数Re=12 500的情况下,开展了动波浪壁波动速度w=0、0.062 5、0.125、0.187 5 m/s四个工况的计算分析,并比较了不同波动速度对流场结构、升力、阻力特性的影响。结果表明:动波浪壁圆柱能有效抑制流动的分离,消除交替脱落的尾涡,从而消除周期振荡的升力;在消除卡门涡街的同时,圆柱后驻点处的涡量值随波动速度增加而增加,其原因在于波形移动加大了壁面流体的速度,从而减小了圆柱前后的压力差,减小了阻力;随着波动速度的增大,平均阻力系数呈明显下降趋势,当波动速度为来流速度的1.5倍时,平均阻力系数相对于光滑圆柱下降了53.76%。     

Random dynamic response of a tethered buoyant platform production riser

A new normal mode spectral analysis method is presented for calculating r.m.s. riser deflections, bending stresses and lower ball joint angles. Forces on the riser consist of: (a) non-linear fluid drag taking account of the relative velocity due to tethered buoyant platform (TBP) motion, riser elastic deflection and wave induced fluid velocity, (b) wave induced fluid acceleration, (c) inertia forces due to TBP acceleration, and (d) buoyancy. The non-linear fluid drag forces are linearized using Tung and Wu's approximation based on the r.m.s. relative fluid velocity and current. A wide range of results is presented for risers in water depths up to 1000 m and it is observed that 6 normal modes are sufficient for calculating bending stresses. A static analysis is also presented for bending stresses due to wave and current induced drag forces and riser offset.     

Response cumulant analysis of a linear oscillator driven by Morison force

A frequency-domain cumulant spectral analysis method is developed in this study to estimate the higher-order statistics of the linear oscillator responses driven by Morison wave force. The fourth-order cumulant function of the nonlinear drag force is formulated in terms of the autocorrelation functions of water particle velocity. Price's theorem is applied to evaluate the associated higher-order joint moments. Three-dimensional Fourier Transforms are employed to obtain the trispectra of Morison force and oscillator responses. The estimated force and response kurtosis are in good agreement with those obtained from time-domain simulations; while the proposed method is found to be much more efficient. The numerical results also show that the drag force cubicization based on the least square approximation results in an overestimation of the kurtosis values; in addition, it is necessary to include the joint moments of order higher than eighth.     

风暴潮和天文潮条件下的底摩擦的研究

由海底摩擦与平均流速的平方成正比的公式,对底摩擦的性质(主要对拖曳系数C_0)进行讨论。研究在风暴潮和天文潮的条件下,海底摩擦与风速,风向和海深等因素的关系,得到有关奇异区的存在等结论,说明在整个海区内拖曳系数不为常数。     

基于“黑格比”和“灿都”台风期间湍流数据的曳力系数和动力粗糙度长度参数化研究*

海面的曳力系数和空气动力学粗糙度长度是计算海气动量、感热和水汽通量交换必需的参数。基于在“黑格比”和“灿都”台风期间收集的涡动相关系统观测数据, 文章研究了10m风速和摩擦速度之间、10m风速和曳力系数之间、以及10m风速和动力粗糙度长度之间的参数化关系。结果表明: 曳力系数和摩擦速度及10m风速之间存在抛物线关系, 动力粗糙度长度与摩擦速度及10m风速之间存在自然指数关系; 临界摩擦速度为0.83m·s^-1, 临界10m级风速为23.69m·s^-1。     

A three-dimensional modeling of multidirectional random wave diffraction by rectangular submarine pits

A three-dimensional modeling of multidirectional random-wave diffraction by a group of rectangular submarine pits is presented in this paper. The fluid domain is divided into N interior regions representing the pit area and an overall exterior region separated by the imaginary pit boundaries. In the interior region, the analytical expressions of the Fourier series expansion for velocity potentials in the pit regions have been derived with the unknown coefficients determined from a series of Green's function based boundary integral equations. The boundary integral approach has also been applied to obtain the velocity potential and free-surface elevation in the exterior region. The Pierson–Moskowitz (P–M) frequency spectrum was selected for the random wave simulation using the superposition of solutions of a finite number of decomposed wave components. Numerical results for the cases of regular waves and random waves are presented to examine the influences of the pit geometry and incident wave condition on the overall wave field. The general diffraction pattern of alternate bands of increase and decrease of relative wave height in front of the pit system can be observed. It is found that, in the shadow region, the relative wave height is reduced. As the number of pit increases, the effectiveness of reducing the relative wave height behind the multiple-pit system increases. However, the relative wave height within the pit area and in front of the leading pit shows increasing trend. It is noticed that under the random-wave condition, the level of increase and decrease of the relative wave height due to the existence of submarine pits is less pronounced than that observed from results in regular-wave condition.     

三维数值模式用于海底摩擦系数的研究

本文讨论了在风暴潮和潮汐作用下海底摩擦力与平均流速的关系公式,即;利用湍流能量损耗理论得到了一个新的求拖曳系数C_b的公式;并且通过一个三维模式,在理想的矩形海区中计算了各种条件下的C_b分布。     

Wave-induced surface drift of an inextensible thin film

In this study, the surface drift of an inextensible film due to a series of progressive gravity waves is investigated both analytically and experimentally. A second approximation of the conformal mapping that transforms the progressive sinusoidal surface to the horizontal axis is applied, thus allowing the analysis to formally accommodate a boundary layer thickness that is much less than the wave height. By computing the stream function to the third order that is an order higher than the past analysis, a pressure component in phase with the wave slope is revealed. The pressure force generated is comparable to the bottom shear on the thin film induced by the moving fluid and thus cannot be ignored. Based on the combined forces on the surface firm, a mean drift is estimated by assuming that the opposing force is due to the viscous drag induced by the drift motion. The experimental results show that the computed drift velocity based on the present study mostly underestimates the experimental observations, but it is in closer agreement than the classical Phillips' 7/4 estimate.     

一个湍能封闭模型对风暴潮海底底应力的应用研究

将一个三维湍能封闭模型应用于开阔海区的风暴潮，通过数值计算探讨了Ｔａｙｌｏｒ底摩擦二次率的拖曳系数随空间的分布及拖曳系数与水深、海底粗糙度、风向和风速等因素的关系。本文对底摩擦二次率的可靠性做了评价。     

Multidimensional stochastic linearisation of drag forces

A number of different methods for linearisation of two- and three-dimensional drag forces with and without current are described. Numerical results from a comparison between the methods based on mean square error and invariance properties are presented. Computationally efficient formulas for the linearisation matrices of the two most promising methods have been derived. It is also shown that the minimum mean square linearisation matrix for fully correlated velocity components is non-unique.     

Wave damping over artificial Posidonia oceanica meadow: A large-scale experimental study

An experimental study, conducted in the large wave flume of CIEM in Barcelona, is presented to evaluate the effects of Posidonia oceanica meadows on the wave height damping and on the wave induced velocities. The experiments were performed for irregular waves from intermediate to shallow waters with the dispersion parameter h/λ ranging from 0.09 to 0.29. Various configurations of the artificial P. oceanica meadow were tested for two stem density patterns (360 and 180 stems/m²) and for plant's height ranging from 1/3 to 1/2 of the water depth.The results for wave height attenuation are in good agreement with the analytical expressions found in literature, based on the assumption that the energy loss over the vegetated field is due to the drag forces. Based on this hypothesis, an empirical relationship for the drag coefficient related to the Reynolds number, Re, is proposed. The Reynolds number, calculated using the artificial P. oceanica leaf width as the length scale and the maximum orbital velocity over the meadow edge as the characteristic velocity scale, ranges from 1000 to 3500 and the drag coefficient C_d ranges from 0.75 to 2.0.The calculated wave heights, using the analytical expression from literature and the proposed relationship for the estimation of C_d, are in satisfactory agreement with those measured. Wave orbital velocities are shown to be significantly attenuated inside the meadow and just above the flume bed as indicated by the calculation of an attenuation parameter. Near the meadow edge, energy transfer is found in spectral wave velocities from the longer to the shorter wave period components. From the analysis it is shown that the submerged vegetation attenuates mostly longer waves.     

Laboratory study on wave dissipation by vegetation in combined current–wave flow

Coastal wetlands such as salt marshes and mangroves provide valuable ecosystem services including coastal protection. Many studies have assessed the influence of plant traits and wave conditions on vegetation-induced wave dissipation, whereas the effect of tidal currents is often ignored. To our knowledge, only two studies investigated wave dissipation by vegetation with the presence of following currents (current velocity is in the same direction as wave propagation) (Li and Yan, 2007; Paul et al., 2012). However, based on independent experiments, they have drawn contradictive conclusions whether steady currents increase or decrease wave attenuation. We show in this paper that this inconsistency may be caused by a difference in ratio of imposed current velocity to amplitude of the horizontal wave orbital velocity. We found that following currents can either increase or decrease wave dissipation depending on the velocity ratio, which explains the seeming inconsistency in the two previous studies. Wave dissipation in plant canopies is closely related to vegetation drag coefficients. We apply a new approach to obtain the drag coefficients. This new method eliminates the potential errors that are often introduced by the commonly used method. More importantly, it is capable of obtaining the vegetation drag coefficient in combined current–wave flows, which is not possible for the commonly used calibration method. Based on laboratory data, we propose an empirical relation between drag coefficient and Reynolds number, which can be useful for numerical modeling. The characteristics of drag coefficient variation and in-canopy velocity dynamics are incorporated into an analytical model to help understand the effect of following currents on vegetation-induced wave dissipation.     

The motion of a 9.1 m yacht hull buoy moored in open sea

A 9.1 m yacht hull was instrumented to measure its three-dimensional motion when moored in the open sea. The hull was deployed on three occasions for a total period of about 2 months and encountered a wide range of wind-wave conditions including a strong gale. The data have been analysed to give the response for each component of motion in terms of amplitude and relative phases. The hull motion is compared spectrally to the waves observed by a nearby Waverider. The hull was found to behave as a surface-keyed buoy, with a well defined response for a wide range of conditions. The presence of a resonance in pitch and roll is evident in the data with typical rms values being 5° and 10°, respectively, for significant wave height of 5 m. From data on the mooring dynamics it is concluded that the peaks observed in the tension are a result of the viscous drag opposing the change in the catenary of the mooring and the slow drift oscillations of the buoy. This type of hull is a versatile and economical candidate as a platform for meteorological and oceanographic instrumentation.     

分隔板对Spar平台涡激运动响应影响的分析研究

当流体流经单柱式结构物时,由于流体黏性和逆压梯度的存在,会产生非定常的升力、阻力和涡旋脱落,即涡激运动现象,对一座Truss Spar平台的硬舱部分附加长度为1.0D(D为硬舱直径)的刚性来流侧分隔板,基于开源平台OpenFOAM,采用基于剪切应力运输的延迟分离涡模拟(SST-DDES)方法,在不可压缩黏性流场中,对其进行三维数值模拟,以研究在不同流速下,来流侧分隔板对Spar平台涡激运动特性和运动响应的影响。结果表明：在较高流速下,横荡周期减小22.21%,横荡最大幅值减小81.3%。说明在较高流速下,附加分隔板有助于减少Spar平台的运动响应幅值。     

Frequency domain analysis of dynamic response of drag dominated offshore structures

The paper describes a method for stochastic representation of the hydrodynamic drag forces on offshore structures subjected to irregular waves. It is shown that, for the case of zero current, it is possible to construct a genuinely quadratic representation of the drag force which reproduces the statistical properties of the standard formulation of the drag force very closely, and which at the same time has sufficient flexibility to ensure a spectral density that accurately approximates the desired force spectrum. The distinct advantage of the new representation is that it brings dynamic analysis of extensive linear structures back into the frequency domain.     

The cross-flow drag on a manoeuvring ship

In this paper, an analysis is given of the experimentally derived local lateral force on a manoeuvring ship as a reaction to the ship's lateral velocity. The tests were performed with models consisting of several segments. Special attention is paid to the longitudinal distribution of the non-linear component of the lateral force, the so-called cross-flow drag. This aspect is of utmost importance when the non-linear contribution becomes dominant as will occur in a tight turn during which the ship's drift velocity becomes relatively large compared to the ahead speed.