Expanded mild-slope equations for the analysis of wave-induced ship motion in a harbor (original) (raw)
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Coastal Engineering 1994, 1995
A numerical method has been developed for the analysis of ship motions in a harbor with arbitrary bathymetry. A BEM-based 3-D model, applied partially to a near-field surrounding a ship, is combined with a FEM-based 2-D model, utilized in the remainder of harbor domain. This combination may achieve an efficient computation of the ship motions with taking into account of wave deformation in a harbor. Preliminary examinations have been performed to investigate appropriate location of a matching boundary where these two models are coupled. It is found that, for reliable prediction, (2 ~ 3)ft (h: water depth) is required for the distance between the matching boundary and a body. The numerical results of added mass and damping coefficients for a rectangular floating body in a rectangular basin are then compared with those obtained from a conventional numerical model. Favorable agreement between the results verifies the present numerical method. Ship motions in a harbor with slowly varying depth are also demonstrated.
Numerical Simulation of the Behaviour of a Moored Ship Inside an Open Coast Harbour
2020
Sea waves inside harbors can affect scheduled port operations. Hence it is important to correctly predict and characterize the wave field inside ports and to describe the movements of the ship and forces acting upon it. A classical approach is to assume that shipwave interaction is linear, [1]. Then it is possible to decompose it in the so-called radiation and diffraction problems. Numerical models that solve such problems have been developed and used by the offshore industry for quite a while, [2], to study the interaction of sea-waves with floating objects. However, these models cannot be used to solve the diffraction problem of ships inside harbor basins where nearby reflecting boundaries and shallow depths create very complex nonlinear wave fields. A new set of procedures using coupled models is proposed in this work. First, a Boussinesqtype finite element wave propagation model is used to determine the wave field in the numerical domain containing the harbor. Then the velocity ...
Numerical study of propagation of ship waves on a sloping coast
Ocean Engineering, 2006
The aim of this paper is to investigate the propagation of ship waves on a sloping coast on the basis of results simulated by a 2D model. The governing equations used for the present model are the improved Boussinesq-type equations. The wave breaking process is parameterized by adding a dissipation term to the depth-integrated momentum equation. To give the boundary conditions at the ship location, the slender-ship approximation is used. It was verified that, although ship waves are essentially transient, the Snell's law can be applied to predict crest orientation of the wake system on a sloping coast. Based on simulated results, an applicable empirical formula to predict the maximum wave height on the slope is introduced. The maximum wave height estimated by the proposed method agrees well with numerical simulation results.
Numerical analysis of wave hazards in a harbor
Science China Earth Sciences, 2012
Resonance may occur when the periods of incoming waves are close to the eigen-periods of harbor basin. The amplified waves by resonance in harbor will induce serious wave hazards to harbor structures and vehicles in it. Through traditional theoretical approaches, the eigen-periods of harbor basin with regular shapes can be obtained. In our study, we proposed a numerical model to simulate the behavior characteristics of the harbor waves. A finite difference numerical model based on the shallow water equations (SWE) is developed to simulate incoming tsunami and tidal waves. By analyzing the time series data of water surface wave amplitude variations at selected synthetic observation locations, we estimate the wave height and arrival time in coastal area. Furthermore, we use frequency spectrum analysis to investigate the natural frequencies from the data recorded at the synthetic observation stations.
Simulation of wave action on a moored container carrier inside Sines’ Harbour
Maritime Technology and Engineering, 2014
The integrated numerical tool SWAMS (Simulation of Wave Action on Moored Ships) is used to simulate the behavior of a moored container carrier inside Sines' Harbour. Wave, wind, currents, floating ship and moorings interaction is discussed. Several case scenarios are compared differing in the layout of the harbour and wind and wave conditions. The several harbour layouts correspond to proposed alternatives for the future expansion of Sines' terminal XXI that include the extension of the East breakwater and of the quay. Additionally, the influence of wind on the behavior of the ship moored and the introduction of pre tensioning the mooring lines was analyzed. Hydrodynamic forces acting on the ship are determined using a modified version of the WAMIT model. This modified model utilizes the Haskind relations and the non-linear wave field inside the harbour obtained with finite element numerical model, BOUSS-WMH (Boussinesq Wave Model for Harbors) to get the wave forces on the ship. The time series of the moored ship motions and forces on moorings are obtained using BAS solver.
On the modeling of wave–current interaction using the elliptic mild-slope wave equation
Ocean Engineering, 2005
Methods to incorporate the effect of ambient currents in the prediction of nearshore wave transformation are developed. This is accomplished through the construction of a finite-element coastal/harbor wave model based on an extended mild-slope wave-current equation that includes wave breaking. Improved boundary conditions are used to provide more accurate forcing and to minimize spurious wave reflections from the boundaries. Multiple nonlinear mechanisms, appearing both in the governing equations and in the boundary conditions, are handled successfully and efficiently with iterative techniques. The methods are tested against results from other types of models based on parabolic approximations or Boussinesq equations for three wave-current problems of common interest and varying complexity. While indicating good agreement in general, the analysis also highlights the limitations of parabolic approximation models in case of strong local currents and velocity shear. We also consider the harbor engineering problem pertaining to waves approaching an inlet with a jettied entrance, where wavecurrent interaction can create a complex wave pattern that adversely affects small craft navigation and causes scouring. The role of ebb and flood currents on wave transformation and on breaking in the vicinity of the inlet is investigated using the model in conjunction with hydraulic laboratory data. It is found that although the ebb currents cause larger waves outside the inlet, much of the wave energy is soon dissipated due to breaking; during the flood tide, in contrast, more wave energy can penetrate into the inlet throat. q Ocean Engineering 32 (2005) 2135-2164 www.elsevier.com/locate/oceaneng 0029-8018/$ -see front matter q
Numerical Investigation of Motion Response of Two Model Ships in Regular Waves
In this paper, the sea keeping performances of two model ships in regular waves are studied by our in-house solver naoe-FOAM-SJTU based on OpenFOAM code package. Volume of Fluid (VOF) method is used to capture the free interface and Finite Volume Method (FVM) is adopted as the discretization scheme. Different wave conditions are set by the wave generation and damping module in the solver. The heave and pitch are simulated, and green water is found during the ship motion. The function of bulbous bow for that is discussed.
Applied Ocean Research, 2003
In the present work, a coupled-mode technique is applied to the transformation of ship's waves over variable bathymetry regions, characterised by parallel depth-contours, without any mild-slope assumption. This method can be used, in conjunction with ship's near-field wave data in deep water or in constant-depth, as obtained by the application of modern (linearised or non-linear) ship computational fluid dynamic (CFD) codes, or experimental measurements, to support the study of wave wash generated by fast ships and its effects on the nearshore/coastal environment. Under the assumption that the ship's track is straight and parallel to the depth-contours, and relatively far from the bottom irregularity, the problem of propagation-refraction-diffraction of ship-generated waves in a coastal environment is efficiently treated in the frequency domain, by applying the consistent coupled-mode model developed by Athanassoulis and Belibassakis [J. Fluid Mech. 1999;389] to the calculation of the transfer function enabling the pointwise transformation of ship-wave spectra over the variable bathymetry region. Numerical results are presented for simplified ship-wave systems, obtained by the superposition of source-sink Havelock singularities simulating the basic features of the ship's wave pattern. The spatial evolution of the ship-wave system is examined over a smooth but steep shoal, resembling coastal environments, both in the subcritical and in the supercritical case. Since any ship free-wave system, either in deep water or in finite depth, can be adequately modelled by wavecut analysis and suitable distribution of Havelock singularities e.g. as presented by Scrags [21st Int. Conf. Offshore Mech. Arctic Eng., OMAE2002, Oslo, Norway, June 2002], the present method, in conjunction with ship CFD codes, supports the prediction of ship wash and its impact on coastal areas, including the effects of steep sloping-bed parts.
A 3D time-domain Rankine source method is developed to study the hydrodynamic loads and motions of a moored ship in shallow water waves in head sea conditions. Both the wave steepness and ship motions relative to the ship's draft are assumed small and the exact free-surface and body-boundary conditions are expanded about the mean surface by a Taylor series. A formulation correctly to second order in the wave steepness is adopted. A fourth-order Runge–Kutta method is used to time integrate the boundary conditions and the six degree of freedom motion equations. It is found that the water depth has significant effects on the hydrodynamic coefficients, especially on the vertical modes of motions. The linear horizontal motions of a moored ship have distinct increment in shallower water depth in the low-frequency domain. Further, the horizontal slow-drift excitation forces increase significantly with decreasing water depth and the second-order velocity potential gives dominant contribution in a frequency range of importance for moored ships in shallow water. Lastly, the slowly varying motions of an LNGC is simulated and the satisfactory agreements with experiments demonstrate that the present method can predict the slowly varying motions of a moored ship in finite-amplitude shallow water waves with acceptable results. Keywords Boundary element method (BEM) · Response amplitude operator (RAO) · Slow-drift excitation forces · Wave-drift damping · Quadratic transfer function (QTF)
Computational and experimental study on local ship loads in short and steep waves
Journal of Marine Science and Technology, 2014
Currently, little information exists on the validity of interface-capturing methods in predicting local ship wave loads in short and steep waves. This study compares computational and experimental results in such a case (kA = 0.24, L wave /L ship = 0.16). The results allow the variation of wave loading between ten locations in the bow area of the ship to be observed. The computations were performed with an unstructured RANS solver that models free-surface flows with a volume-of-fluid method. In the model tests, the wave loads were measured with pressure sensors. The analysis of the results focuses on the wave conditions and on the pressure histories of the local wave loads. The computational and experimental results are in good qualitative agreement and encourage the further use of the computational results.