Study on the Simulation and Run-up of Ship Waves of Express Liners in the Zhujiang Delta

Ship waves are observed with wave-generating techniques by way of simulating express liners in the Zhujiang Delta.The analog test study of ship waves is conducted in a wave flume and a wave basin respectively. Thus, different wave elements and different incident angles of ship waves are decided; so are different slopes of protection, the plafform, width of plafform, and the influence over the ship wave run-up on protection from armor coat structure. The empirical relation-

VELOCITY FIELD IN SHIP WAVES ON THE VISCOUS FLUID

From the Navier-Stokes equations, the integral expressions of the free-surface elevation and the velocity field in ship waves of a moving waterborne body are obtained. Next, Lighthill' s two-stage scheme is employed to change the above-mentioned integral expressions to algebraic expressions. Compared with the results obtained when the seawater is idealized to an inviscid fluid, the singularities are dispelled or weakened, and the accuracy of the digit information of ship waves is improved.

WAVE EQUATION MODEL FOR SHIP WAVES IN BOUNDED SHALLOW WATER

Ships were modelled as moving pressure disturbances on the free surface of a shallow water basin in the present paper. The moving pressure generating waves were subjected to the reflection of land boundaries and the radiation of open boundaries. This paper proposed and examined a wave equation model (WEM) to solve the shallow water equations with moving surface pressures simulating ship waves in a bounded shallow water region. The Galerkin finite element method was used to solve a second order wave equation for the free surface elevations and the hydrodynamic pressure of the ship bottom simultaneously. Horizontal velocities were obtained from the momentum equations. Numerical solutions of Series 60 C B=0.6 ships moving with the depth Froude number of F h= 0.6, 1.0, 1.3 in a rectangular shallow water harbor were investigated. Three dimensional surface elevation profiles and the depth averaged horizontal velocities were analysed. The numerical results characterised very well the ship waves in shallow water. Strong boundary reflection waves were found in the case of high depth Froude number (F h=1.3). Waves generated by the interactions of two ships moving in the same directions and in the opposite directions were also numerically investigated in the present study.

A STUDY OF VELOCITY FIELD IN SHIP WAVES

Searching ships on the ocean with the technique of the oceanic remote sensing, one must be requensted to know not only the amplitude of ship waves, but also horizontal velocities. In this article Lighthill's two-stage scheme was employed to change the integral expressions into algebraic expressions for the velocity components, so the obtained results are very succinct.

SOME PROBLEMS ABOUT SHIP WAVES

Several problems about ship waves were discussed in the dissertation: (1) Transient ship waves from calmness to the generation of steady-state ship waves were described. (2) The procedure of the formation of the V-shaped steady-state ship waves were clearly shown, and the difference of ship waves on an inviscid fluid and on a viscous fluid was exmined. (3) With the Lighthill two-stage scheme, the algebraic expression for ship waves on a viscous fluid of finite depth was obtained. (4) Singularity on the two boundaries of the ship waves was treated.

AN ASYMPTOTIC SOLUTION OF VELOCITY FIELD IN SHIP WAVES

The stationary phase method in conventional Lighthill＇s two-stage scheme to get the expressions of the velocity field was given up in this paper. The method that Ursell had used in deducing the elevation expression of ship wave was adopted, and an asymptotic solution of velocity field of ship waves on an inviscid fluid that is perfectly fit for the region inside and outside the critical lines was obtained. It is very convenient to be used in SAR technique.

ENVIRONMENTAL AND TOPOGRAPHIC INFLUENCES ON ATMOSPHERIC INTERNAL SHIP WAVES

A theoretical model was used to investigate the influences of environmental and topographic parameters on the atmospheric three-layer internal ship waves. The results show that both the wavelength and the wedge angle decrease with an increase in the Scorer parameter, and the rate of changes in the wavelength and wedge angle are also alike. The results also show that the wedge angle decreases with an increase in the width of mountain, but the wavelength varies little with it. It is suggested that the wedge angle is determined by the ratio of the wavelength to the scale of the mountain. Besides, numerical sensitivity experiments were performed to test the former numerical experiments. The simulated results are consistent with the analytical results.

Basic models of farfield ship waves in shallow water

Basic models of the farfield waves created by a monohull ship or a catamaran that travels at a constant speed in calm water of uniform finite depth are considered.A classical basic model is the 1-point ship model introduced by Kelvin in 1887 for deep water and extended to uniform finite water depth by Havelock in 1908.Another basic model is the 2-point ship model,which considers the two dominant waves created by the bow and the stern of a monohull ship or by the twin bows of a catamaran,and therefore accounts for main wave interference effects.These 2-point ship models contain information that cannot be found in the classical patterns for the 1-point ship model commonly used since Kelvin.In particular,whereas Havelock’s classical wave patterns for the 1-point model only depend on the Froude number based on the water depth,the farfield waves for the 2-point models of a monohull ship or a catamaran also depend on the Froude number associated with the length of the monohull ship or the spacing between the twin hulls of the catamaran.Moreover,the‘apparent wake angles’associated with the highest waves that result from constructive wave interferences can greatly differ from the cusp or asymptote angles of Havelock’s wave patterns.

Stationary phase and practical numerical evaluation of ship waves in shallow water

A simple and highly-efficient method for numerically evaluating the waves created by a ship that travels at a constant speed in calm water, of large depth or of uniform depth, is given. The method, inspired by Kelvin＇s classical stationary-phase analysis, is suited for evaluating far-field as well as near-field waves. More generally, the method can be applied to a broad class of integrals with integrands that contain a rapidly oscillatory trigonometric function with a phase function whose first derivative（and possibly also higher derivatives） vanishes at one or several points, commonly called points of stationary phase, with the range of integration.

Wash Waves Generated by High Speed Displacement Ships

It is difficult to compute far-field waves in a relative large area by using one wave generation model when a large calculation domain is needed because of large dimensions of the waterway and long distance of the required computing points. Variation of waterway bathymetry and nonlinearity in the far field cannot be included in a ship fixed process either. A coupled method combining a wave generation model and wave propagation model is then used in this paper to simulate the wash waves generated by the passing ship. A NURBS-based higher order panel method is adopted as the stationary wave generation model; a wave spectrum method and Boussinesq-type equation wave model are used as the wave propagation model for the constant water depth condition and variable water depth condition, respectively. The waves calculated by the NURBS-based higher order panel method in the near field are used as the input for the wave spectrum method and the Boussinesq-type equation wave model to obtain the far-field waves. With this approach it is possible to simulate the ship wash waves including the effects of water depth and waterway bathymetry. Parts of the calculated results are validated experimentally, and the agreement is demonstrated. The effects of ship wash waves on the moored ship are discussed by using a diffraction theory method. The results indicate that the prediction of the ship induced waves by coupling models is feasible.

SURFACE EFFECTS OF INTERNAL WAVE GENERATED BY A MOVING SOURCE IN A TWO-LAYER FLUID OF FINITE DEPTH

Based on the potential flow theory of water waves, the interaction mechanism between the free_surface and internal waves generated by a moving point source in the lower layer of a two_layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface_wave mode and internal_wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr 2. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui_yang.

Capillary-gravity ship wave patterns

Ship wave pattern is a fascinating research topic in the fields of marine hydrodynamics and water waves. Within the pure-gravity wave theory, the ship wave pattern composed of transverse waves and divergent waves appearing on the downstream is confined within a sector symmetrical about the ship track with a half-angle 19°28＇. However, when the surface tension is accounted for, the wave pattern is greatly modified especially at a low translating speed. Besides the minimum speed of capillary waves c_（min）= 0.23 m/s below which waves cannot be generated, there is another critical speed c_（div）= 0.45 m/s associated with the disappearance of divergent waves. In the present paper, the wave patterns created by a steadily translating source are studied, and they are examined with the crestlines obtained from the asymptotic analysis.

WAVE MAKING COMPUTATION IN TIME DOMAIN FOR MULTI-HULL SHIPS

A method Green function satisfying of three-dimensional time domain linear conditions at free surface and body surface boundary was employed to analyze the wave resistance and wave profile of a displacement multi-hull ship. The wave profile induced by a moving time domain point source was compared with those by a Havelock source, and satisfactory results were obtained. The panel method based on the time domain source distribution on the ship mean wetted hull surface was used to perform the wave making com- putations tbr mono-hull ships, catamaran and trimaran. Reasonable results were also obtained. Using the numerical method the wave profile simulations of multi-hull ships for a given Froude number were conducted.

OPTIMIZATION OF A WAVE CANCELLATION MULTIHULL SHIP USING CFD TOOLS

A simple CFD tool, coupled to a discrete surface representation and a gradient based optimization procedure, is applied to the design of optimal hull forms and optimal arrangement of hulls for a wave cancellation multihull ship. The CFD tool, which is used to estimate the wave drag, is based on the zeroth order slender ship approximation. The hu ll surface is represented by a triangulation, and almost every grid point on the surface can be used as a design variable. A smooth surface is obtained via a si mplified pseudo shell problem. The optimal design process consists of two steps . The optimal center and outer hull forms are determined independently in the fi rst step, where each hull forms are determined independently in the first step, where each hull keeps the same displacement as the original design while the wav e drag is minimized. The optimal outer hull arrangement is determined in the se cond step for the optimal center and outer hull forms obtained in the first step . Results indicate that the new design can achieve a large wave drag reduction i n comparison to the original design configuration.

Optimization of the roll motion of box-shaped hull section with anti-rolling sloshing tanks and fins in beam waves

With the development of ocean engineering and demand for safety of the ship and offshore structures, the transportation and storage of liquid have become an important issue nowadays. Furthermore, in order to improve the hydrodynamic performances of the ship and offshore structures, the anti-rolling liquid tanks are often taken into consideration. The internal-external coupling flow effect is vital for the ship and liquid tank designs, especially when the external wave frequency is close to the natural frequency of liquid tanks with a certain filling ratio, large amplitude motions may occur, which is dangerous to some extent. In this paper, the simulation-based-design method is introduced at first, and the verification of the numerical calculation of internal-external coupling flow with liquid tanks is done then. Finally, the filling ratio of the anti-rolling liquid tank and the installation angle of the anti-rolling fins are optimized to reduce the roll motion amplitude of the hull section to the greatest extent under the combined action of the two anti-rolling devices. Optimization results show that the roll motion amplitude of box-shaped hull section can be successfully reduced by reasonably designing the two anti-rolling devices, which can be a reference to the future design of the fishing ship and other ships with anti-rolling devices.

Artificial Boundary Method for Calculating Ship Wave Resistance

The calculation of wave resistance for a ship moving at constant speed near a free surface is considered. This wave resistance is calculated with a linearized steady potential model. To deal with the unboundedness of the physical domain in the potential flow problem, we introduce one vertical side as an artificial upstream boundary and two vertical sides as the artificial downstream boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the potential flow problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. The solution of the variational problem by the finite element method gives the numerical approximation of the potential flow around the ship, which was used to calculate the wave resistance. The numerical examples show the accuracy and efficiency of the proposed numerical scheme.

THE GLOBAL ARTIFICIAL BOUNDARY CONDITIONS FOR NUMERICAL SIMULATIONS OF THE 3D FLOW AROUND A SUBMERGED BODY

We consider the numerical approximations of the three-dimensional steady potential flow around a body moving in a liquid of finite constant depth at constant speed and distance below a free surface in a channel. One vertical side is introduced as the upstream artificial boundary and two vertical sides are introduced as the downstream artificial boundaries. On the artificial boundaries, a sequence of high-order global artificial boundary conditions are given. Then the original problem is reduced to a problem defined on a finite computational domain, which is equivalent to a variational problem. After solving the variational problem by the finite element method, we obtain the numerical approximation of the original problem. The numerical examples show that the artificial boundary conditions given in this paper are very effective.