Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

URANS investigation of the interaction between the free surface and a shallowly submerged underwater vehicle at steady drift

An axisymmetric underwater vehicle (UV) at a steady drift angle experiences the complex three-dimensional crossflow separation. This separation arises from the unfavorable circumferential pressure gradient developed from the windward side toward the leeward side. As is well known, the separated flow in the leeward side gives rise to the formation of a pair of vortices, which affects considerably the forces and moments acting on the UV. In this regard, the main purpose of the present study is to evaluate the role of the leeward vortical flow structure in the hydrodynamic behavior of a shallowly submerged UV at a moderate drift angle traveling beneath the free surface. Accordingly, the static drift tests are performed on the SUBOFF UV model using URANS equations coupled with a Reynolds stress turbulence model. The simulations are carried out in the commercial code STARCCM+ at a constant advance velocity based on Froude number equal to F_n = 0.512 over submergence depths and drift angles ranging from h = 1.1D to h = ∞ and from β = 0 to β = 18.11°, respectively. The validation of the numerical model is partially conducted by using the existing experimental data of the forces and moment acting on the totally submerged bare hull model. Significant interaction between the low-pressure region created by the leeward vortical flow structure and the free surface is observed. As a result of this interaction, the leeward vortical flow structure appears to be largely responsible for the behavior of the forces and moments exerted on a shallowly submerged UV at steady drift.     

Modeling of iceberg drift in the marginal ice zone of the Barents Sea

The paper is focused on the analysis of the drift of tabular iceberg observed in 2009 in the marginal ice zone of the North-West Barents Sea. Momentum balance equations are derived from the Kirchhoff equations describing plane motion of solid body in an ideal fluid. Field works performed on the drift iceberg and on the drift icenear the iceberg are described. Results of the field works and numerical simulations of the iceberg drift and rotation are performed and discussed. It is shown that acceleration of water flow around the iceberg has visible influence on the iceberg drift. Kinetic energy balance of drift iceberg is used to estimate the forces applied to the iceberg by the drift ice.     

基于GPU加速的Boussinesq类波浪传播变形数值模型

Boussinesq波浪模型是一类相位解析模型,在时域内求解需要较高的空间和时间分辨率以保证计算精度。为提高计算效率,有必要针对该类模型开展并行算法的研究。与传统的中央处理器(CPU)相比,图形处理器(GPU)有大量的运算器,可显著提高计算效率。基于统一计算设备架构CUDA C语言和图形处理器,实现了Boussinesq模型的并行运算。将本模型的计算结果同CPU数值模拟结果和解析解相比较,发现得到的结果基本一致。同时也比较了CPU端与GPU端的计算效率,结果表明,GPU数值模型的计算效率有明显提升,并且伴随数值网格的增多,提升效果更为明显。     

礁坪上波浪传播的数值模拟

本文基于具备间断捕捉能力的二阶全非线性Boussinesq数值模型,对规则波和随机波在礁坪地形上的传播变形进行了数值模拟。该模型采用高阶有限体积法和有限差分方法求解守恒格式的控制方程,将波浪破碎视为间断,同时采用静态重构技术处理了海岸动边界问题。重点针对礁坪上波浪传播过程中的波高空间分布和沿程衰减,礁坪上的平均水位变化,以及波浪能量频谱的移动和空间差异等典型水动力现象开展数值计算。将数值结果与实验结果对比,两者吻合情况良好,验证了模型具有良好的稳定性,具备模拟破碎波浪和海-岸动边界的能力,能较为准确地模拟波浪在礁坪地形上的传播过程中发生的各种水动力现象。     

泉州湾赤潮藻类优势种细胞密度回归方程研究

于2006年5-11月对东海泉州湾赤潮监控区四个监测站位开展赤潮常规监测。根据监测结果,分别以各站位23项水质理化生物环境因子指标为自变量,相应赤潮藻类优势种的细胞密度为因变量,进行多元逐步回归分析,建立了各站位优势种中肋骨条藻(Skeletonema costatum)、太平洋海链藻(Thalassiosira pacifica)、微小原甲藻(Prorocentrum minimum)、尖刺拟菱形藻(Pseudo-nitzschia pungens)、丹麦细柱藻(Leptocylindrus danicus)和旋链角毛藻(Chaetoceros curvisetus)等的细胞密度多参量回归方程。结果表明,所有回归方程的复相关系数都接近于1,方差分析的结果均为回归极显著,表明所建立的回归方程可作为相应赤潮优势种细胞密度预报方程的高度有效性,将对今后泉州湾的赤潮预报提供良好的指导作用。     

New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systems

On the tangent bundle TS^N-1 of the unit sphere S^N-1, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel--Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.     

A Time-Domain Coupled Model for Nonlinear Wave Forces on A Fixed Box-Shaped Ship in A Harbor

A 2-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear wave forces on a fixed box-shaped ship in a harbor.The domain is divided into an inner domain and an outer domain.The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations.The other area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions.Along the interface boundaries between the inner domain and the outer domain,the volume flux is assumed to be continuous and the wave pressures are equal.Relevant physical experiment is conducted to validate the present model.It is shown that the numerical results agree with the experimental data.Compared with the coupled model with the flow in the inner domain governed by the Laplace equation,the present coupled model is more efficient and its solution procedure is more simple,which is particularly useful for the study on the effect of the nonlinear wave forces on a fixed box-shaped ship in a large harbor.     

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.     

A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations

A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.