Analysis of some key parametrizations in a beach profile morphodynamical model

A numerical process-based model to forecast beach profile morphodynamics has been developed. In the present paper, an analysis of various modelling approaches and key parametrizations involved in the estimation of the wave-driven current and the suspended sediment concentration is carried out.Several resolution techniques for the 1DV horizontal (i.e., in the x-direction perpendicular to coastline) momentum equation governing the Mean Horizontal Velocity (MHV) are analysed. In the first kind of techniques, the mean horizontal velocity is computed from the momentum equation, whereas the Mean Water Level (MWL) is computed using a parametrization of the depth-averaged momentum equation. Two boundary or integral conditions are thus needed. In the second kind, both mean horizontal velocity and mean water level gradient in the x-direction are the unknowns of the momentum equation, thus, three boundary or integral conditions are needed. Various additional conditions are discussed. We show that using a technique of the first kind is equivalent to imposing the difference between the surface and the bottom shear stresses in the 1D vertical equation. Both techniques lead to results that are in good agreement with the Delta Flume experimental data, provided the Stokes drift flow discharge is imposed as an additional condition. The influence of the breaking roller model and of the turbulent viscosity parametrization are also analysed.Suspended sediment transport by the mean current and wave-induced bedload transport are taken into account in the sediment flux. Three turbulent diffusivity parametrizations are compared for suspended sediment concentration estimations. A linear profile for the turbulent diffusivity taking into account the wave bottom shear stress and the surface wave breaking turbulence production is shown to give the best results. Using experimental data, we put forward the poor estimation of the bottom sediment concentration given by the three implemented parametrizations. We thus propose a new parametrization relying on a Shields parameter based on the breaking roller induced surface shear stress. Using this new parametrization, the bottom profile used in the tests keeps its two bars which disappear otherwise. However, the morphodynamical model still overestimates the bars offshore motion, a bias already observed in other models.     

A modeling study of the dynamics of pore water seepage from intertidal marsh sediments

A numerical boundary integral equation model has been used to simulate tidally driven transient variations in pore water seepage from salt marsh sediments into tidal channels and its subsequent recharge by tidal inundation. In general the results show that the maximum seepage discharge occurs at or near the intersection of the creek bank and the channel water surface. Over a tidal cycle typically two-thirds of the total seepage discharge occurs through the creek bank with only about a third discharging from the channel bottom. Of the creek-bank discharge up to a third occurs through the seepage face that develops above the tide line at tidal stages below mean tide. These results indicate that placement of seepage meters only on the channel bottom will not give samples or measures representative of the total seepage. Of the total recharge only about 5% occurs through the upper part of the creek bank with the remainder infiltrating vertically through the marsh platform during early stages of tidal submergence. For the platform recharge about 80% occurs within 3 m of the creek bank. Thus, most of the water that seeps out of marsh sediments is derived from sediments that lie within several meters of the creek bank and accordingly has had a relatively short residence (one to two years) in the marsh. Compared to the distal portion of the marsh this relatively rapid flushing may enhance the productivity of Spartina alterniflora in the creek-bank environment and control the differential generation of radium quartet isotopes.     

A new approximation for ocean waves propagating over a beach with variable depth

In this paper, the phenomenon of ocean waves propagating over a beach with variable water depth is re-examined. Based on the assumption of shallow water, a linearised shallow water equation is solved with an arbitrary beach profile. These irregular beach profiles form a set of partial differential equation with variable coefficient as the governing equation, which is the main obstacle in obtaining analytical solutions. In this paper, two families of beach profile are used as examples. A parametric study is conducted to investigate the influence of the beach profiles on the water surface elevation (η) and velocities (u).     

On the numerical modeling of tsunami wave generation and propagation

Abstract

In this article three main stages of tsunami wave evolution are investigated. At first, the development of disturbances from a given patched elevation of the bottom surface in an incompressible nonviscous fluid of the uniform depth is considered. Then, a tsunami wave diffraction by underwater bottom elevation or cavity is investigated. In this case the shallow water equations are already used, and it is supposed that a cylindrical wave is spread from patched water elevation over the epicentrum. Last, the tsunami propagation and transformation in a shallow water region and its run‐up on a beach are investigated on the basis of the improved shallow water theory, taking into consideration the nonlinear and dispersive terms of higher order. The proposed theory is tested in a problem of collisions of two solutions. Solutions of the first and the second problems are obtained by the method of integral Laplace's transformation with following numerical inversion of transformations. A finite difference method for a solution of the last problem is used.     

Unsteady ship waves in shallow water of varying depth based on Green–Naghdi equation

Based on Green–Naghdi equation this work studies unsteady ship waves in shallow water of varying depth. A moving ship is regarded as a moving pressure disturbance on free surface. The moving pressure is incorporated into the Green–Naghdi equation to formulate forcing of ship waves in shallow water. The frequency dispersion term of the Green–Naghdi equation accounts for the effects of finite water depth on ship waves. A wave equation model and the finite element method (WE/FEM) are adopted to solve the Green–Naghdi equation. The numerical examples of a Series 60 (C_B=0.6) ship moving in shallow water are presented. Three-dimensional ship wave profiles and wave resistance are given when the ship moves in shallow water with a bed bump (or a trench). The numerical results indicate that the wave resistance increases first, then decreases, and finally returns to normal value as the ship passes a bed bump. A comparison between the numerical results predicted by the Green–Naghdi equation and the shallow water equations is made. It is found that the wave resistance predicted by the Green–Naghdi equation is larger than that predicted by the shallow water equations in subcritical flow , and the Green–Naghdi equation and the shallow water equations predict almost the same wave resistance when , the frequency dispersion can be neglected in supercritical flows.     

Hydrodynamic characteristics of ship sections in shallow water with complex bottom geometry

The method of boundary integral equation developed by the authors was applied for computing inertial and damping characteristics of ship sections for the cases of multi-stepped and inclined bottoms. Comparative calculations for three typical ship hull sections were performed and analyzed. The frequency-dependent data computed for these ship sections can be used to assess the bottom geometry's influence onto the ship motions in waves by means of the strip theory. Limiting values of the same characteristics corresponding to the close-to-zero frequency can also be used for estimation of hydrodynamic forces in manoeuvring over shallow and confined waterways.     

Numerical simulation of PMM tests for a ship in close proximity to sidewall and maneuvering stability analysis

As the maneuverability of a ship navigating close to a bank is influenced by the sidewall, the assessment of ship maneuvering stability is important. The hydrodynamic derivatives measured by the planar motion mechanism (PMM) test provide a way to predict the change of ship maneuverability. This paper presents a numerical simulation of PMM model tests with variant distances to a vertical bank by using unsteady RANS equations. A hybrid dynamic mesh technique is developed to realize the mesh configuration and remeshing of dynamic PMM tests when the ship is close to the bank. The proposed method is validated by comparing numerical results with results of PMM tests in a circulating water channel. The first-order hydrodynamic derivatives of the ship are analyzed from the time history of lateral force and yaw moment according to the multiple-run simulating procedure and the variations of hydrodynamic derivatives with the ship-sidewall distance are given. The straight line stability and directional stability are also discussed and stable or unstable zone of proportional-derivative (PD) controller parameters for directional stability is shown, which can be a reference for course keeping operation when sailing near a bank.     

Recovering the functional form of the nonlinear roll damping of ships from a free-roll decay experiment: An inverse formulism

The purpose of this paper is to identify the functional form of the nonlinear roll damping for a particular ship based on an experiment. The problem of damping identification is formulated as an integral equation of the first kind. However, the solution of the problem lacks stability properties, due to the ill-posedness of the first-kind integral equation. To resolve this problem, a stabilization technique (known as a regularization method) is applied to the present problem of the identification of nonlinear damping. The identified results for nonlinear roll dampings are compared with those from a conventional roll identification method. The findings of the present study are validated by the direct comparison of experimental data on free-roll decay motion with the numerically simulated results.     

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.     

A parabolic equation extended to account for rapidly varying topography

In this paper, following the procedure outlined by Li (1994. An evolution equation for water waves. Coastal Engineering, 23, 227-242) and Hsu and Wen (2000. A study of using parabolic model to describe wave breaking and wide-angle wave incidence. Journal of the Chinese Institute of Engineers, 23(4), 515–527) and Hsu and Wen (2000) the extended refraction–diffraction equation is recasted into a time-dependent parabolic equation. This model, which includes higher-order bottom effect terms, is extended to account for a rapidly varying topography and wave energy dissipation in the surf zone. The importance of the higher-order bottom effect terms is examined in terms of the relative water depth. The present model was tested for wave reflection in a number of different environments, namely from a plane slope with different inclinations, from a patch of periodic ripples. The model was also tested for wave height distribution around a circular shoal and wave breaking on a barred beach. The comparison of predictions with other numerical models and experimental data show that the validity of the present model for describing wave propagation over a rapidly varying seabed is satisfactory.     

An efficient method for the numerical calculation of viscous effects on transient long waves

Previous studies have shown that the Boussinesq equations can be used to calculate the instantaneous bottom shear stress induced by transient or periodic waves. The bottom friction term occurs as a convolution integral in time in the continuity equation. The exact numerical integration of a convolution integral demands large computational resources, which makes the method less useful for large scale computations. In this paper we explore how the value of the convolution integral can be estimated if we only use the values of the variables in a limited number of time steps, and discuss the accuracy and computational cost of this method.     

Numerical Simulation of Wave Field at the Kemena River Mouth in Kalimantan Island

-By use of the parabolic equation of numerical simulation of wave which is suitable forlarge-angle propagation and Crank-Nicolson differential method,the wave field at the Kemema Rivermouth has been studied for analysis of sediment movement in the area.In order to reflect wave energy lossaccurately,the Bretchneider-Reid formula is quoted and the friction coefficient in the formula is discussedin this paper.The calculation results indicate that the wave becomes a little damped at the mouth ofKemena River influenced by the topography and bottom friction,and the wave at the east beach is higherthan that at the west beach,because the east beach extends out.     

On the determination of modal attenuation coefficients andcompressional wave attenuation profiles in a range-dependent environmentin Nantucket Sound

Techniques for determining modal attenuation coefficients and the compressional wave attenuation profile of the bottom in shallow water are presented. The input data consists of spatially well-sampled measurements of the pressure field versus range due to a monochromatic point source, which can be provided by either real or synthetic aperture horizontal arrays. Several methods are described for obtaining modal attenuation coefficients from the pressure field or its Hankel transform. The bottom attenuation profile is related to the modal attenuation coefficients through an integral equation that is solved using linear inverse theory. The methods are demonstrated using both noise-free and noisy synthetic data. The results of inverting experimental data from Nantucket Sound at 140 Hz and 220 Hz are presented. including the resolution and variance estimates of the inferred bottom attenuation profiles. Separation of the contributions of other attenuating mechanisms that can be confused with compressional wave attenuation (shear, rough surface scattering) is also discussed     

Study on submarine cable tension during laying

In order to design submarine optical-fiber cable, it is very important to clarify the cable tension and fiber elongation during laying because the fiber elongation allowance is very small. When submarine cable is being laid from a cable ship, cable weight in water plus such additional tension as bottom tension caused by the negative slack and tension due to ship motion work upon the cable [1]. Cable tension changes during laying were theoretically studied. This paper quantitatively clarifies bottom tension dependence at the touchdown point caused by the negative slack upon both water depth and ship velocity. It is shown that the shallower the water depth is and the faster the ship velocity is, the larger the bottom tension is. The theoretical bottom tension showed good agreement with the experimental value measured during sea trials on laying submarine optical-fiber cable [2], [3]. This paper also describes the correlation between cable, ship motion, and cable tension vibration by examining experimental results. It quantitatively clarifies the tension vibration magnitude.     

Fast computation of the transient motions of moving vessels in irregular ocean waves

A fast time-domain method is developed in this paper for the real-time prediction of the six degree of freedom motions of a vessel traveling in an irregular seaway in infinitely deep water. The fully coupled unsteady ship motion problem is solved by time-stepping the linearized boundary conditions on both the free surface and body surface. A velocity-based boundary integral method is then used to solve the Laplace equation at every time step for the fluid kinematics, while a scalar integral equation is solved for the total fluid pressure. The boundary integral equations are applied to both the physical fluid domain outside the body and a fictitious fluid region inside the body, enabling use of the fast Fourier transform method to evaluate the free surface integrals. The computational efficiency of the scheme is further improved through use of the method of images to eliminate source singularities on the free surface while retaining vortex/dipole singularities that decay more rapidly in space. The resulting numerical algorithm runs 2–3 times faster than real time on a standard desktop computer. Numerical predictions are compared to prior published results for the transient motions of a hemisphere and laboratory measurements of the motions of a free running vessel in oblique waves with good agreement.     

琼东南盆地北礁凹陷梅山组单向迁移水道特征及成因探讨

深水区重力流与底流交互作用的过程、响应及动力学机制是海洋沉积学研究的前沿和薄弱环节。本文通过三维地震资料,在深水区北礁凹陷南西部梅山组发现多条相间分布的长条形顺直强振幅水道,垂直于西沙隆起(南部隆起)北斜坡走向,向南西方向单向迁移,水道具有南西陡(凹岸或陡岸)北东缓(凸岸或缓岸)的特征,该类水道分为侵蚀界面和水道砂-堤岸泥过渡复合体系两个单元,侵蚀界面在凹岸的削截反射明显多于凸岸,水道砂-堤岸泥过渡复合体振幅强度由凹岸强振幅逐渐过渡为凸岸弱振幅。分析认为,该类水道发育于中中新世半深海环境,不同于向底流下游方向单向迁移的峡谷,它们向底流上游方向发生单向迁移,并提出其成因模式:前期来自南部的浊流下切形成负向地貌单元(水道),底流对这一地貌单元进行改造,形成迎流面缓(凸岸)背流面陡(凹岸)的地貌,同时驱使浊流上部顺底流方向偏移,形成溢岸浊流沉积,致凹岸沉积速率低,凸岸沉积速率高,这样就迫使水道逆底流方向偏移。沉积物源、中层水相关底流、古气候和海平面的变化、北礁凸起古地形控制是该区单向迁移强振幅水道发育的因素。本研究在南海首次发现这种向底流上游方向单向迁移的水道,是底流与重力流交互作用的新型类型,对古海洋、古气候研究,深水油气勘探有着重要的意义,希望引起地质学家的重视。     

Simulation of wave breaking effects in two-dimensional elliptic harbor wave models

A technique is developed for including the effects of dissipation due to wave breaking in two-dimensional elliptic models based on the mild-slope wave equation. This involves exploration of convergence properties pertaining to iteration due to presence of the nonlinear wave breaking parameter in the governing equations as well as new boundary conditions that include wave-breaking effects. Five wave-breaking formulations are examined in conjunction with the resulting model, which is applied to tests involving a sloping beach, a bar-trough bottom configuration, shore-connected and shore-parallel breakwaters on a sloping beach, and two real-world cases. Model results show that three of the formulations, when used within the context of the modeling scheme presented here, provide excellent results compared to data.     

Wave resistance of a hovercraft moving in water with nonrigid bottom

Surface waves generated by a moving ship in water of finite depth are affected by the rheological properties of the movable bottom. The aim of this work is to evaluate the wave resistance exerted on a hovercraft modeled as a two-dimensional pressure distribution moving on the free surface of water with nonrigid bottom. Analysis of three-dimensional flows in two-fluid layers of finite depths is performed by assuming an inviscid upper layer (water) and a viscous lower layer (nonrigid bottom). Numerical calculations show that the maximum wave resistance occurs in the vicinity of the critical Froude number F=1. This maximum value decreases as the muddy bottom becomes less rigid.     

Ship motions and sea loads in restricted water depth

The influence of the sea bottom on ship motions and sea loads is examined. It is described how to calculate the vertical motions and loads for a ship with non-zero forward speed in regular waves by use of sttip theory and fluid finite element method. Results of such calculations are shown. The effects of shallow water are significant as is seen from several figures.     

A finite volume discretization of the pressure gradient force using analytic integration

Layered ocean models can exhibit spurious thermobaric instability if the compressibility of sea water is not treated accurately enough. We find that previous solutions to this problem are inadequate for simulations of a changing climate. We propose a new discretization of the pressure gradient acceleration using the finite volume method. In this method, the pressure gradient acceleration is exhibited as the difference of the integral “contact” pressure acting on the edges of a finite volume. This integral “contact” pressure can be calculated analytically by choosing a tractable equation of state. The result is a discretization that has zero truncation error for an isothermal and isohaline layer and does not exhibit the spurious thermobaric instability.