An approximated method for the solution of elliptic problems in thin domains: Application to nonlinear internal waves

Realistic numerical simulations of nonlinear internal waves (NLIWs) have been hampered by the need to use computationally expensive nonhydrostatic models. In this paper, we show that the solution to the elliptic problem arising from the incompressibility condition can be successfully approximated by a few terms (three at most) of an expansion in powers of the ratio (horizontal grid spacing)/(total depth). For an n dimensional problem, each term in the expansion is the sum of a function that satisfies a one-dimensional second-order ODE in the vertical direction plus, depending on the surface boundary condition, the solution to an n-1 dimension elliptic problem, an evident saving over having to solve the original n-dimensional elliptic problem. This approximation provides the physically correct amount of dispersion necessary to counteract the nonlinear steepening tendency of NLIWs. Experiments with different types of NLIWs validate the approach. Unlike other methods, no ad hoc artificial dispersion needs to be introduced.     

Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

Nonlinear random wave-induced drag force on a vegetation field

This paper provides a practical method by which the drag force on a vegetation field beneath nonlinear random waves can be estimated. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (Mendez, F.J., Losada, I.J., Losada, M.A., 1999. Hydrodynamics induced by wind waves in a vegetation field. J. Geophys. Res. 104 (C8), 18383–18396). Effects of nonlinear waves are included by using Stokes second order wave theory where the basic harmonic motion is assumed to be a stationary Gaussian narrow–band random process. An example of calculation is also presented.     

Nonlinear transfer function modelling of beach morphology at Duck,North Carolina

This paper presents a simple nonlinear data-based modelling approach for predicting the beach profile volume at Duck, North Carolina, USA. The state-dependent parameter form of the general transfer function (SDP TF) model is used to describe nonlinearity influencing these morphological data in two case examples. Case 1 investigates the nonlinearity associated with the dependency of wave forcing on the preceding beach volume. Case 2 investigates the ability to model the variables within the well-known diffusion equation for beach volume using this data-based approach. The results of this study show that the SDP TF approach can be used successfully to develop statistically robust models for describing nonlinearity in beach morphological systems. Furthermore, these models are shown to predict the beach volumes over both short (1 month ahead) and long (2 years ahead) time periods, and thus show great potential for practical applications in coastal zone management and engineering.     

基于NLCCA的中国夏季降水与东亚夏季风关系的探讨

运用一种基于人工神经网络的非线性典型相关分析方法(NLCCA),对中国夏季降水与东亚夏季风之间的非线性关系进行了分析。结果表明,夏季降水对东亚夏季风的响应具有一定的非线性,当夏季风较强与较弱时,对应的中国夏季降水异常分布呈现明显的不对称性。夏季降水与夏季风之间的关系可分离为线性响应和非线性响应,其中非线性响应部分占总方差贡献的52.1%,说明我国夏季降水异常分布与东亚夏季风相互之间的关系既有线性特征也有非线性特征,非线性响应略显重要。     

Numerical modeling of nonlinear water waves over heterogeneous porous beds

The transformation of nonlinear water waves over porous beds is studied by applying a numerical model based on Chen's [2006. Fully nonlinear Boussinesq-type equations for waves and currents over porous beds. Journal of Engineering Mechanics, 132:2, 220–230] Boussinesq-type equations for highly nonlinear waves on permeable beds. The numerical model uses a high-order time-marching solution and fourth-order finite-difference schemes for discretization of first-order spatial derivatives to obtain a computational accuracy consistent with the model equations. By forcing the wave celerity and spatial porous-damping rate of the linearized model to match the exact linear theory for horizontal porous bed over a prescribed range of relative depths, the values of the model parameters are optimally determined. Numerical simulations of the damped wave propagation over finite-thickness porous layer demonstrate the accuracy of both the numerical model and governing equations, which have been shown by prior theoretical analyses to be accurate for both nominal and thick porous layers. These simulations also elucidate on the significance of the higher-order porous-damping terms and the influence of the hydraulic parameters. Application of the model to the simulation of the wave field around a laboratory-scale submerged porous mound provides a measure of its capability, as well as useful insight into the scaling of the porous-resistance coefficients. For application to heterogeneous porous beds, the assumption of weak spatial variation of the porous resistance is examined using truncated forms of the governing equations. The results indicate that the complete set of Boussinesq-type equations is applicable to porous beds of nonhomogeneous makeup.     

非线性效应对浅水水波变形的影响

本文采用波数矢量无旋和波能守恒方程建立了一个考虑非线性作用的浅水水波变形数值模型,模型中采用Ｂａｔｔｊｅｓ关系与波数矢量无旋,波能守恒方程一起来求解波浪在浅水中变形的波浪要素,在波能守恒方程中考虑了底摩擦的影响。利用本文提出的数值模型对一个斜坡浅滩水域波浪折射绕射现象进行了验证,验证计算中用一个非线性经验弥散关系近似浅水水波变形的非线性效应并与用线性弥散关系的计算结果进行了比较,结果说明使用非线性     

深水声学拖曳系统

介绍了我国自主设计和研制的深水声学拖曳系统,它的最大工作水深4000m,安装有高分辨率测深侧扫声纳,可在近海底工作获得高分辨率的海底地形地貌和温盐深等数据.它的测深覆盖范围600m,侧扫覆盖范围800m,垂直航迹分辨率5cm,最小可检测高度10cm,测深分辨率高于目前的多波束测深系统.该系统已进行了湖试和海上锚泊试验.该系统的研制成功将对开展大陆架勘查,探测和开发国际海底资源发挥重要作用,拖曳系统中高分辨率测深侧扫声纳还可装船安装,在大陆架水域进行高分辨率海底地形地貌测绘.     

A nonlinear PDE formulation for offshore vessel pipeline installation

In this paper a nonlinear dynamic PDE formulation for a pipe string suspended from a pipelay vessel to the seabed in a pipelay operation is developed. This model extends a three-dimensional beam model capable of undergoing finite extension, shearing, twist and bending, to apply for marine applications by adding the effects of restoring forces, hydrodynamic drag and seabed interaction. The model is validated against the natural catenary equation and the FEM code RIFLEX. The model is extended to include the pipelay vessel dynamics by applying a potential theory formulation of a surface vessel, suited for dynamic positioning and low speed maneuvering, as a boundary condition for the PDE. This system is found to be input-output passive and stable. Pipeline installation applications where the presented model is suited are e.g., analysis and simulation of the installation operation, operability analysis, hardware-in-the-loop (HIL) testing for vessel control systems, and automation of the pipelay operation.     

Nonlinear adaptive control of an underwater towed vehicle

This paper addresses the problem of simultaneous depth tracking and attitude control of an underwater towed vehicle. The system proposed uses a two-stage towing arrangement that includes a long primary cable, a gravitic depressor, and a secondary cable. The towfish motion induced by wave driven disturbances in both the vertical and horizontal planes is described using an empirical model of the depressor motion and a spring-damper model of the secondary cable. A nonlinear, Lyapunov-based, adaptive output feedback control law is designed and shown to regulate pitch, yaw, and depth tracking errors to zero. The controller is designed to operate in the presence of plant parameter uncertainty. When subjected to bounded external disturbances, the tracking errors converge to a neighbourhood of the origin that can be made arbitrarily small. In the implementation proposed, a nonlinear observer is used to estimate the linear velocities used by the controller thus dispensing with the need for costly sensor suites. The results obtained with computer simulations show that the controlled system exhibits good performance about different operating conditions when subjected to sea-wave driven disturbances and in the presence of sensor noise. The system holds promise for application in oceanographic missions that require depth tracking or bottom-following combined with precise vehicle attitude control.