LINEAR WAVES IN ROTATIONAL HOMOGENEOUS FLUID WITH UNIFORM WATER DEPTH Ⅱ. POSSIBLE WAVES FILTERED OUT BY THE ASSUMPTION OF HYDROSTATIC PRESSURE

In the first part of our studies, the unified solutions of existing waves have been obtained by using the linear wave equations without making the assumptions of irrotation and hydrostatic pressure. In this paper, the second part of our studies, we shall devote to linear long wave equations without the assumption of hydrostatic pressure. All the solutions in the case of ω=f are found. A set of solutions is also obtained, with a similarity to the unified solutions of the Sverdrup waves and the Poincare waves, but the corresponding waves represented by such a set have a different vertical structure of velocities. The set is not included in the solutions of linear long wave equations under the assumption of hydrostatic pressure and, therefore, is regarded as possible waves filtered out by the assumption of hydrostatic pressure.     

Vertical 2D Modeling of Free Surface Flow with Hydrodynamic Pressure Using SIMPLE Arithmetic in σ Coordinates

A numerical model for shallow water flow has been developed based on the unsteady Reynolds-averaged Navier-Stokes equations with the hydrodynamic pressure instead of hydrostatic pressure assumption. The equations arc transformed into the a-coordinate system and the eddy viscosity is calculated with the standard k -ε turbulence model. The control volume method is used to discrete the equations, and the boundary conditions at the bed for shallow water models only include vertical diffusion terms expressed with wall functions. And the semi-implicit methed for pressure linked equation arithmetic is adopted to solve the equations. The model is applied to the 2D vertical plane flow of a current over two steep-sided trenches for which experiment data are available for comparison and good agreement is obtained. And the model is used to predicting the flow in a channel with a steep-sided submerged breakwater at the bottom, and the streamline is drawn.     

A Vertical Two-Dimensional Model to Simulate Tidal Hydrodynamics in A Branched Estuary

A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The goveming equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are govemed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations,tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.     

A Hybrid Finite-Volume and Finite Difference Scheme for Depth-Integrated Non-Hydrostatic Model

A depth-integrated, non-hydrostatic model with hybrid finite difference and finite volume numerical algorithm is proposed in this paper. By utilizing a fraction step method, the governing equations are decomposed into hydrostatic and non-hydrostatic parts. The first part is solved by using the finite volume conservative discretization method, whilst the latter is considered by solving discretized Poisson-type equations with the finite difference method. The second-order accuracy, both in time and space, of the finite volume scheme is achieved by using an explicit predictor-correction step and linear construction of variable state in cells. The fluxes across the cell faces are computed in a Godunov-based manner by using MUSTA scheme. Slope and flux limiting technique is used to equip the algorithm with total variation dimensioning property for shock capturing purpose. Wave breaking is treated as a shock by switching off the non-hydrostatic pressure in the steep wave front locally. The model deals with moving wet/dry front in a simple way. Numerical experiments are conducted to verify the proposed model.     

A hydraulic hammer corer utilizing hydrostatic energy for hard seafloor sediment coring

The paper presents the design and preliminary test results of a corer used for hard seafloor sediments sampling.Generally the sediment cores are provided by either gravity-type coring or deep-ocean drilling for a range of studies.However,in consideration of the operability and available sample length in collecting hard sediments,these methods exhibit no advantages.In this paper,a new corer which can exploit both hydrostatic energy and gravity energy for hard sediments coring is presented.The hydrostatic energy is provided by pressure differential between ambient seawater pressure and air pressure in an empty cavity.During sampling process,the corer penetrates into the sediment like a gravity corer and then automatically shifts to the percussion mode.The experiments in the laboratory indicate that the corer can complete 40 cycles in the sea with a cycle time of 2.8 seconds in percussion mode and impact the sample tube with the velocity of 0.2 m/s during each cycle.Besides,its adjustable falling velocity can make the corer achieve the maximum efficiency in coring different sediments.     

Buckling Properties of Water-Drop-Shaped Pressure Hulls with Various Shape Indices Under Hydrostatic External Pressure

The water-drop-shaped pressure hull has a good streamline, which has good application prospect in the underwater observatory. Therefore, this study conducted analytical, experimental and numerical investigation of the buckling properties of water-drop-shaped pressure hulls under hydrostatic pressure. A water-drop experiment was conducted to design water-drop-shaped pressure hulls with various shape indices. The critical loads for the water-drop-shaped pressure hulls were resolved by using Mushta...     

Investigation of Scouring Mechanism Around A Circular Pier

In the present study,the flow field around a circular pier is investigated with experimental measurements and numerical simulations.The transient flow patterns during erosion are studied in detail.The results show that the traditional equations of particle motion are not perfect for the calculation of the sand motion under this complex flow situation.The scouring agents,such as turbulent intensity,the fluctuating pressure and the vertical pressure gradient,having many effects on the sand motion with the increasing scouring depth,need to be considered in modifying the traditional model.     

Three Dimensional Baroclinic Numerical Model for Simulating Fresh and Salt Water Mixing in the Yangtze Estuary

For simulating fresh and salt water mixing in estuaries, a three dimensional nonlinear baroclinic numerical model is developed, in which the gradients of horizontal pressure contain the gradient of barotropic pressure arising from the gradi-ent of tidal level and the gradient of baroclinic pressure due to the gradient of salinity. The Eulerian-Lagrangian method is employed to descretize both the momentum equations of tidal motion and the equation of salt water diffusion so as to im-prove the computational stability and accuracy. The methods to provide the boundary conditions and the initial conditions are proposed, and the criterion for computational stability of the salinity fields is presented. The present model is used for modeling fresh and salt water mixing in the Yangtze Estuary. Computations show that the salinity distribution has the characteristics of partial mixing pattern, and that the present model is suitable for simulalion of fresh and salt waler mixing in ihe Yanglze Esluary.     

Effect of Longitudinal Plastic Bending of Pipeline on Buckle Propagation Pressure

A plastic ring-beam model simulating the longitudinal transition zone of submarine pipelines in the buckle propagation is presented. The nonlinear relationships between the buckle propagation pressure and the length of the transition zone and the position parameter of the longitudinal plastic hinge are derived using the energy principle. The related values are obtained by means of solving a set of nonlinear equations. The model conforms better to reality than the ring models for considering the effect of the longitudinal plastic bending of the transition zone. The computations for some stainless steel and aluminium tubes with different geometrical parameters are performed. The results obtained agree better with the experimental results than existing theoretical predictions.     

Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary

In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.     

The numerical study of wave-induced pore water pressure response in highly permeable seabed

The coupling numerical model of wave interaction with porous medium is used to study waveinduced pore water pressure in high permeability seabed.In the model,the wave field solver is based on the two dimensional Reynolds-averaged Navier-Stokes(RANS) equations with a k-ε closure,and Forchheimer equations are adopted for flow within the porous media.By introducing a Velocity-Pressure Correction equation for the wave flow and porous flow,a highly efficient coupling between the two flows is implemented.The numerical tests are conducted to study the effects of seabed thickness,porosity,particle size and intrinsic permeability coefficient on regular wave and solitary wave-induced pore water pressure response.The results indicate that,as compared with regular wave-induced,solitary wave-induced pore water pressure has larger values and stronger action on seabed with different parameters.The results also clearly show the flow characteristics of pore water flow within seabed and water wave flow on seabed.The maximum pore water flow velocities within seabed under solitary wave action are higher than those under regular wave action.     

Ultimate Load Capacity of Offshore Pipeline with Arbitrary Shape Corrosion Defects

A set of generalized solutions are proposed for estimating ultimate load capacity of pipeline with arbitrary corrosion shapes subjected to combined internal pressure, axial force and bending moment. Isotropic and anisotropic material characteristics in longitudinal and circumferential direction of pipeline are also considered in the proposed equations. Simplified numerical method is used to solve the generalized expressions. The comparisons of numerical results based generalized solutions and full-scale experimental results are carried out. The predicted results agree reasonably well with the experiment results. Meanwhile, the effects of corrosion shapes and locations on the ultimate load capacity are studied.     

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.     

Ship Hull Slamming Analysis with Nonlinear Boundary Element Method

A boundary element method is developed for calculating the flare ship hull slammingproblem.The nonlinear free surface elevation and the linear element assumption are employed.The meth-od has been verified by comparisons with results for the water entry of wedges with various deadriseangles.Numerical results show that the pressure distribution varies greatly with the ship hull with differentcurvilinear equations,and the slamming features are also different.From the numerical simulation,the au-thors found that the structural damage of the flare hull might be caused by the increasing hydrodynamicpressure over an extensive area on the flare when the upper part of the flare comes into contact with water.     

The computation of maximum wind speeds of typhoon

-At present, it is still difficult to obtain an accurate maximum wind speed of typhoon with modern means,such as satellite survey , radar tracing and airplane reconnaissance. The performance of statistical equation established with observational maximum wind speed and the central pressure of typhoon is unstable ,and it is unreliable in operational use. Therefore a general pressure field model of typhoon is introduced in this paper based on atmospheric motion equations and formulas are derived for computing the maximum wind speed around typhoon center over sea surface . The theoretical curves derived from these formulas are in good agreement with those using the statistic empirical curves of typhoon pressure-wind relations over the western Pacific. Tests were conducted for typhoons which occurred in 1973 and in 1983 and the strongest typhoons selected each year during 1970 and 1978,the results were satisfactory. Meanwhile the analyses of computing results showed that the effect of Coriolis force could be     

STUDY ON CALCULATION OF OCEAN CURRENT VELOCITY

"Dynamic Computation" used to be calculate only the geostrophic current velocityand the Ekman's drift-current theory applied to compute only the wind-drift current ve-locity are the two basic theorems widely used for easily calculating the current velocitiesof different kinds of ocean currents. But they have their own defects. For easily calcula-ting both the velocity of ocean current produced by the uneven density distribution of seawater and that by the wind and atmospheric pressure of sea surface, the author presentsin this paper a method for solving the equations of motion in consideration of vertical tur-bulence only by using the values of horizontal pressure gradient and the coefficient ofeddy viscosity determined according to a certain fact. With this method We have calculatedthe velocity of ocean current in Kuroshio in the East China Sea, and obtained satisfac-     

Numerical Modelling of Standing Waves with Three-Dimensional Non-Linear Wave Propagation Model

Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate the wave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, .and the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions     

Direct numerical simulation of interaction between wave and porous breakwater based on N-S equation

In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference method. The free surface is tracked by the VOF method. The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method. Finally, compared with the physical model test results of wave flume, the numerical model established in the present study is validated.     

New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions

Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.     

Nonlinear Analysis of Nearshore Wave Height Variation Due to Shoaling

Wave formulae derived from the dispersion relation for cnoidal waves are used to find an analytical solution to the problem of nearshore wave height variation on a simple topography, i. e., with an incrementally constant slope. The solution accounts for shoaling, frictional dissipation and will be sufficiently accurate for practical purposes considering the simplified assumptions which are necessary for the treatment of this problem by any method.