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.

A Study on the Estimation of Ship Waves Interaction with the Sloping Banks of the Channel

The problem of shore wash in environmental engineering is connected in particular with the effect of waves generated by the ships and fast speed boats. Another problem is protection of ＂Marines＂ with anchored boat against waves. Sloping banks provoke unfavorable transformation of waves. Simultaneously sloping bank is the factor which significantly complicates prediction of wave pattern in numerical analysis. The purpose of present paper is to demonstrate the results of numerical investigation of ship waves pattern in constrain water area with slope banks by panel method for non-linear ship waves calculation usually applied for ship hull perfection as routine instrument of towing tanks technology. The method initially developed for calculation of ship hull waves in inviscid infinite fluid was adapted to meet boundary conditions on slope banks. Verification of the method was done for 60-series ship in rectangular channel. Development of wave pattern generated by two ship of different types--monohull ferries and river catamaran was investigated. It was found that ship waves height significantly increased due to slopping banks comparing with case of deep water and shallow water rectangular channel.

B-Spline Approximation of Ship Waves on the Free Surface

We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.

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.

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.

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.

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.

Experimental and Numerical Studies of the Wave-Induced Responses of a River-to-Sea Ship

The ship motions and wave-induced loads of a new type of river-to-sea ship are investigated experimentally and numerically. A river-to-sea ship is an unconventional type of container ship characterized by high breadth to draft ratio and low length to breadth ratio, which makes it more prone to hydroelasticity than conventional ships of the same size. A segmented model was tested under two loading conditions, namely, ballast and loaded conditions, to determine the vertical motions and wave-induced loads under each condition. Results are compared with numerical simulations in the frequency domain. The wave-induced responses are calculated by a nonlinear time domain code at each time step. The response amplitude operators of vertical ship responses in regular waves are analyzed, and the wave-induced responses are consistent with the experimental results.

Model Test and Design of the Wave Energy System on "Central Fairway No. 1" Light Ship

This paper presents the test of a ship model for the design of a backward-bent duct oscillating water column type wave energy conversion system, to supply electric power for a light ship. This system suggests a new way to produce electric power automatically for large light ships.

NUMERICAL STUDY OF SQUARE-STERN SHIP WAVE IN SHALLOW WATER

The calculation of the water wave generated by a square ship in shallow water was studied by using the shallow water equations with moving pressure. The moving ship in the shallow water was considered as the moving pressure on free surface. The finite element method with moving grids was used to solve the shallow water equations based on wave equation model. A non-reflection boundary condition was imposed on the open boundaries surrounding the ship. 3-D surface elevations, depth-averaged horizonal velocities were presented. It is found that the wave resistance coefficients, draft change and pitch angle vary rapidly in neighborhood of critical flow. The wave resistance coefficients draft change and pitch angle of square-stern ship are larger than those of sharp-stern ship with the same hull structure at same speed.

River bank protection from ship-induced waves and river flow

A new equation is proposed for the design of armor units on protected river banks under the combined action of ship-induced waves and river flow.Existing observed field and experimental data in the literature have been examined and a valuable database has been developed.Different conditions,including the river water depth,flow velocity,river bank slope,Froude number,wave height,wave period,and wave obliquity have been considered.Results from an empirical equation (Bhowmik,1978) that only considers the maximum wave height and river bank slope have been compared with the results calculated by the newly developed equation.Calculated results have also been verified against field data.Results show that not only the maximum wave height and river bank slope but also the water depth,flow velocity,wave length,wave obliquity,and wave period are important parameters for predicting the mean diameter of the armor units,highlighting the multivariate behavior of protecting the river bank in the presence of ship-induced waves and river flow velocity.

An Application of the Real Free Surface Boundary Condition in Calculation of Ship wave Problem

A real free surface boundary condition,taking the viscous effects and surface tension into account,is applied to the nonlinear calculation of wave making resistance.It may provide more information about the character of the nonlinear ship wave and be helpful to improving the stability,convergence and local wave profile in potential calculation of the nonlinear ship wave.The wave making calculations for Series 60 are presented.

Numerical study on wave loads and motions of two ships advancing in waves by using three-dimensional translating-pulsating source

A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to mea- sure the wave loads and the free motions for a pair of side-by- side arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating （3DP） source Green function. Numer- ical resonances and peak shift can be found in the 3DP pre- dictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free sur- face and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two ves- sels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.

Nonlinear Optimization Method of Ship Floating Condition Calculation in Wave Based on Vector

Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.