Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability, the convective derivatives in the free-surface boundary conditions are treated using an upwind-biased stencil. Instead of solving for the radiation impulse response functions, a pseudo-impulsive Gaussian type displacement is employed in order to tailor the frequency-content to the discrete spatial resolution. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth-order convergence of the calculations on simple geometries is demonstrated, along with a nearly linear scaling of the solution effort with increasing grid resolution. The code is validated by comparison with analytical and semi-analytical solutions using submerged and floating closed-form geometries. Calculations are also made for a modern bulk carrier, and good agreement is found with experimental measurements.     

Linear analysis of air cushion vehicle seakeeping response

A linearized analysis of the response of an air cushion vehicle running in waves is described. The analysis uses the linear systems approach where the vehicle is considered to be a “black box”, i.e. the response characteristics are determined experimentally from input-output relationships. The wave forces and moments are expressed in a form that produces the proper limiting behavior for infinite wavelength. Predicted motion response is shown to compare well with experimental data.     

Numerical analysis of the influence of fixed hydrofoil installation position on seakeeping of the planing craft

This paper analyzes the hydrodynamic performance of a planing craft with a fixed hydrofoil in regular waves. Numerical simulations are carried out based on a RANS-VOF solver to study the hydrodynamic performance of the planing craft and the influence of the fixed hydrofoil on its seakeeping. To validate the numerical method, a series of hydrodynamic experiments of a bare planing craft without the hydrofoil were carried out, from which the seakeeping performance of the planing craft was recorded, the numerical method based on overset grid was compared with the experiment and verified reliable. Eight hydrofoil design cases were then studied, whereby, their seakeeping performance in regular wave conditions were predicted through the numerical method which has been verified reliable and compared with each other. Effects of hydrofoil parameters, such as angle of attack and installation height, on the seakeeping performance were investigated. Finally, the suitable installation parameters which can optimize the performance of hydrofoil and reduce the negative influence are verified. The influence of the speed on the effect of the hydrofoil and the flow field around the planing craft are also investigated.     

A multi-scale high-order recursive filter approach for the sea ice concentration analysis

With the development and deployment of observation systems in the ocean, more precise passive and active microwave data are becoming available for the weather forecasting and the climate monitoring. Due to the complicated variability of the sea ice concentration(SIC) in the marginal ice zone and the scarcity of high-precision sea ice data, how to use less data to accurately reconstruct the sea ice field has become an urgent problem to be solved. A reconstruction method for gridding observations ...     

Wave height statistics for seakeeping assessment of ships in the Adriatic Sea

The paper presents methodology and results of the development of sea states statistics for the Adriatic Sea. Such statistics is still lacking despite a need of the shipping industry. The presented study is based on the Atlas of Climatology containing statistics of sea states observations in the Adriatic Sea made by merchant ships during the period of 15 years. The results, presented in the Atlas in the form of “wave roses”, are digitalized and empirical frequencies of sea state occurrences are obtained. The 3-parametric Weibull distribution is then fitted through empirical data points enabling the “smoothening” of the histogram. The resulting histogram is compared with other studies for the long-term prediction of the sea states in the Adriatic Sea. The paper concludes with the discussion on the accuracy and applicability of the results.     

Numerical investigation of the seakeeping behavior of a catamaran advancing in regular head waves

A numerical study was undertaken in order to assess the capability of an unsteady RANS code to predict the seakeeping characteristics of a high-speed multi-hull vessel in high sea states. Numerical analysis includes evaluation of ship motions, effects of wave steepness on ship response, catamaran natural frequency and added resistance in waves. Computations were performed for the DELFT 372 catamaran by the URANS solver CFDSHIP-Iowa V.4. The code was validated with encouraging results for high ship speeds (0.3≤Fn≤0.75) and high wave amplitudes (0.025≤Ak≤0.1). Comparison with strip theory solutions shows that the RANS method predicts ship motions with higher accuracy and allows the detection of nonlinear effects. Current computations evidence that heave peaks occur at resonance for all Fn, and reach the absolute maximum at Fn=0.75. Maximum pitch occurs at frequencies lower than resonance, for each speed, and absolute maximum occurs at medium Fn=0.6. Maximum added resistance, R_aw, was computed at Fn=0.45, which, interestingly, is near the catamaran Fn_coincidence. Overall, we found similar results as Simonsen et al. (2008) for KCS containership, though, herein, a multi-hull geometry and higher speeds were tested. Also, our results are useful to further evaluate the exciting forces and their correlation with f_e and λ/L_pp.     

On the numerical prediction of seakeeping and of structural loads of high-speed vessels

The applicability of an efficient 3D numerical method for the evaluatfion of the seakeeping performance and structural loads of advanced high-speed vessels is investigated. A semi-empirical approach to account for the viscous flow effects on ship's behavior at speed is presented and discussed. Numerical results are compared with model tests for two high-speed monohull vessels with satisfactory agreement.     

A new methodology developed by cetena to assess the seakeeping behaviour of marine vessels

The paper describes an analytical method to determine an operability index for a marine vehicle when its geometric characteristics, the geographical area in which the vessel is supposed to operate, and the limiting criteria for operations are known. The computer program based on strip theory provides reliable results not only for conventional hullforms, but also for catamarans, offshore vehicles, etc. The results are presented in the form of figures for different vessels, namely, crane barge, naval vessels and SWATH type catamarans. The authors are of the opinion that the proposed method would provide the designer with a valid tool to improve the seakeeping qualities of a vessel, while taking into account the limiting conditions imposed due to seaway operations.     

Stability analysis of TLP tethers

Compliant offshore TLPs are essentially meant for deep oil/gas exploration and are usually constructed on the seashore and then towed down to the particular location for anchorage. They are connected to the sea bed by means of pretension cables. The increased use of TLPs in deep waters and necessity of reduction of usually high value of pretension make the effect of variable tension in the tether dynamics more significant. This work presents the dynamic analysis of tethers and TLPs considering the linearly varying tension along the tether length. The modal analysis considers a linear cable equation for tether modeling subjected to tension which varies along its length. A Mathieu stability analysis is then performed for TLPs of different shapes and different water depth vis-à-vis of 527.8, 872, and 1200 m respectively to obtain the amplitudes of tether vibrations. The unstable modes of vibration are also verified. The resultant modal forms for the tether's dynamic model are then obtained in form of Bessel's function. From the numerical studies conducted it is seen that increased tether tension not only leads to a stable platform but also improves the stability due to increased hydrodynamic loading contributing to added mass. From the studies conducted it is also seen that the triangular configuration TLPs with increased initial pretension are more stable compared to four leg TLP in the first mode of vibration.     

豪华邮轮耐波性及救生艇砰击载荷特性研究

利用基于三维势流理论的Wasim软件,系统研究了在不同海况下大型豪华邮轮的耐波性能及作用在救生艇上的砰击载荷。首先计算豪华邮轮在规则波和不规则波中的运动响应,分析航速、浪向和海况对豪华邮轮运动响应的影响规律,然后计算救生艇在不同海况下砰击载荷的变化规律,根据变化规律评估救生艇在实际航行中的安全性。结果表明：豪华邮轮运动响应幅值随着航速和海况的增大整体呈增大趋势,规则波中横摇运动响应幅值在浪向90°时最大;当豪华邮轮处于4级和6级海况时救生艇不发生砰击;当豪华邮轮处于8级海况且航速大于10.29 m/s时救生艇发生砰击,为保证救生艇的安全,邮轮应避免在浪向120°和浪向150°下航行,此时建议邮轮以低于12.35 m/s的航速迎浪180°航行。     

Stability analysis of the heave motion of marine cable-body systems

The dynamic stability of the heave motion of marine cable-body systems operating in alternating taut–slack conditions is considered, based upon a single-degree-of-freedom model. In this model the fluid damping is linearised and the cable is replaced by a spring of bi-linear stiffness. The period-one Poincare map is derived, and its stability is analysed by examining its Jacobian matrix. Numerical simulations are also carried out to show the transition from a periodic response to a chaotic one through period doubling.     

Hybrid three-dimensional finite-difference and finite-element analysis of seismic wave induced fluid–structure interaction of a vertical cylinder

The two-dimensional finite-difference scheme has been extended to three dimensions to solve nonlinear hydrodynamic pressures and structural responses of a deformable, vertical and circular surface-piercing offshore cylinder during earthquakes. A complete three-dimensional analysis has been made with both the three-dimensional equations of motion and the simultaneous action of three components of ground acceleration included in the analysis. Not only the magnitude but also the direction of the acting ground motion can be varied with time. The dynamic response of a cylinder is approximated by the displacements in the fundamental modes of vibration. A comparison of the dynamic displacement of the cylinder with and without surrounding sea water has been made. The flexibility of the offshore cylinder can significantly increase the hydrodynamic pressures acting on cylinder faces, that is, the fluid-structure interaction is necessary in offshore cylinder analysis. Although the hydrodynamic pressure induced by the vertical ground acceleration of the El Centro 1979 earthquake is significant, the calculated structural dynamic response of a cylinder is very small and the corresponding resultant hydrodynamic force is almost nil. The hydrodynamic force induced by two-horizontal ground acceleration is about the same as that by three simultaneous components of ground acceleration. For a solid and stubbier circular cylinder, the vertical component of ground acceleration may be neglected.     

粘塑性海冰流变模型的稳定性分析

对Hibler 1977提出的具有粘塑性本构关系的海冰模型进行了修改和稳定性分析.在已有的工作中,应用这样一个粘塑性本构关系进行数值积分时大多都必须引入人工扩散项.这里我们用数值逼近技巧提出计算相邻浮冰之间相互作用力的新方法,并且证明修改后的模型无论是海冰的收敛还是发散流动都是稳定的,模式积分无需引入人工扩散项.以二维...     

A panel-free method for time-domain analysis of the radiation problem

A panel-free method (PFM), based on the desingularized Green’s formulae proposed by Landweber and Macagno, has been developed to solve the radiation problem of a floating body in the time domain. The velocity potential due to a non-impulsive velocity is obtained by solving the boundary integral equation in terms of source strength distribution. The singularity in the Rankine source term of the time-dependent Green function is removed. The geometry of a body surface is mathematically represented by NURBS surfaces. The integral equation can be globally discretized over the body surface by Gaussian quadratures. No assumption is needed for certain degree of approximation of distributed source strength on the body surface. The accuracy of PFM was demonstrated by its application to a classical problem of uniform flow past a sphere. The response function of a hemisphere at zero speed was then computed by PFM. The computed response function, added-mass and damping coefficients are compared with other published results.     

水下悬浮隧道锚索稳定性分析

为研究水下悬浮隧道锚索的稳定性,建立锚索在涡街激励作用下振动的数学方程,采用伽辽金法对其进行化简,锚索振动的稳定性通过Lyapunov指数法进行判断,分析了锚索动静张力比的大小、悬浮隧道系统的阻尼比和锚索参数激励频率对锚索振动稳定性的影响。计算结果表明,锚索振动失稳的范围取决于锚索的动静张力比、锚索的阻尼比和频率比(锚索参数激励频率与锚索1阶模态固有频率的比值);当频率比为1和2左右时,随着锚索动静张力比的增大和阻尼比的减小,锚索逐渐从稳定状态转变为不稳定状态,且锚索的不稳定区域逐渐增大。     

Stability analysis of a two-inlet bay system

The stability analysis for a double-inlet bay system is applied to an inlet system resembling Big Marco Pass and Capri Pass on the lower west coast of Florida. Since the opening of Capri Pass in 1967, the length of Big Marco Pass has increased from 2000 m in 1967 to 3000 m in 1988 and the cross-sectional area has decreased from 1200 m² in 1967 to 1000 m² in 1988. Since 1967, the cross-sectional area of Capri Pass has steadily increased and in 1988 was 700 m². Tides off the inlets are of the mixed type with a diurnal range of 1 m. The gross littoral transport rate in the vicinity of the inlets is estimated at 150,000 m³ yr⁻¹.For each inlet the maximum tidal velocities are calculated as a function of the gorge cross-sectional areas using a lumped-parameter model to describe the hydrodynamics of the flow. In the model it is assumed that the bay level fluctuates uniformly and the bay surface area remains constant. The velocities are used to calculate the tidal maximum of the bottom shear stress in each inlet as a function of the cross-sectional areas of the two inlets (=closure surface). Values of the equilibrium shear stress are derived from an empirical relationship between cross-sectional area and tidal prism for stable inlets along the west coast of Florida. Closure surfaces and equilibrium stress values are calculated for values of friction factors ranging from F=4×10⁻³ to F=6×10⁻³. Using the closure surfaces and equilibrium stress values, the equilibrium flow curve for each inlet is determined. The equilibrium flow curve represents the locus of the combination of cross-sectional areas for which the actual bottom shear stress in the inlet equals the equilibrium shear stress.Based on the equilibrium flow curves and the known values of the cross-sectional areas of the two inlets in 1988, it is expected that, ultimately, Big Marco Pass will close and Capri Pass will remain as the sole inlet with a cross-sectional area of 1250 m² and a maximum tidal velocity pertaining to a diurnal tide of 0.85 m s⁻¹.     

Dispersion and stability analyses of the linearized two-dimensional shallow water equations in Cartesian coordinates

In the present study, a Fourier analysis is used to develop expressions for phase and group speeds for both continuous and discretized, linearized two-dimensional shallow water equations, in Cartesian coordinates. The phase and group speeds of the discrete equations, discretized using a three-point scheme of second order, five-point scheme of fourth order and a three-point compact scheme of fourth order in an Arakawa C grid, are calculated and compared with the corresponding values obtained for the continuous system. The three-point second-order scheme is found to be non-dispersive with grid resolutions greater than 30 grids per wavelength, while both the fourth-order schemes are non-dispersive with grid resolutions greater than six grids per wavelength. A von Neumann stability analysis of the two- and three-time-level temporal schemes showed that both schemes are stable. A wave deformation analysis of the two-time-level Crank–Nicolson scheme for one-dimensional and two-dimensional systems of shallow water equations shows that the scheme is non- dispersive, independent of the Courant number and grid resolution used. The phase error or the dispersion of the scheme decreases with a decrease in the time step or an increase in grid resolution.     

随机波作用下海床动态响应分析

真实的海洋波浪是随机的,而前人对海床的动态响应分析大都是选用线性波或者Stokes波理论,对海床的模拟大都采用Biot拟静力模型,忽略了流体速度及土体位移加速度的影响。联合使用Longuet-Higgins随机波模型(采用Jonswap谱)以及动力u-p形式的海床响应计算模型,使用COMSOL Multiphysics多场耦合软件的PDE模块输入方程进行有限元计算,得到随机波作用下整体海床动态响应结果。将随机波结果与一阶Stokes波和椭圆余弦波结果进行对比,并对渗透系数和饱和度进行参数分析,研究表明渗透系数和饱和度对于随机波作用下海床动态响应影响显著。     

A hybrid spectral/finite-difference large-eddy simulator of turbulent processes in the upper ocean

A three-dimensional numerical model for large-eddy simulation (LES) of oceanic turbulent processes is described. The numerical formulation comprises a spectral discretization in the horizontal directions and a high-order compact finite-difference discretization in the vertical direction. Time-stepping is accomplished via a second-order accurate fractional-step scheme. LES subgrid-scale (SGS) closure is given by a traditional Smagorinsky eddy-viscosity parametrization for which the model coefficient is derived following similarity theory in the near-surface region. Alternatively, LES closure is given by the dynamic Smagorinsky parametrization for which the model coefficient is computed dynamically as a function of the flow. Validation studies are presented demonstrating the temporal and spatial accuracy of the formulation for laminar flows with analytical solutions. Further validation studies are described involving direct numerical simulation (DNS) and LES of turbulent channel flow and LES of decaying isotropic turbulence. Sample flow problems include surface Ekman layers and wind-driven shallow water flows both with and without Langmuir circulation (LC), generated by wave effects parameterized via the well-known Craik–Leibovich (C–L) vortex force. In the case of the surface Ekman layers, the inner layer (where viscous effects are important) is not resolved and instead is parameterized with the Smagorinsky models previously described. The validity of the dynamic Smagorinsky model (DSM) for parameterizing the surface inner layer is assessed and a modification to the surface stress boundary condition based on log-layer behavior is introduced improving the performance of the DSM. Furthermore, in Ekman layers with wave effects, the implicit LES grid filter leads to LC subgrid-scales requiring ad hoc modeling via an explicit spatial filtering of the C–L force in place of a suitable SGS parameterization.