A Simple Eddy Viscosity Model of Rough Turbulent Wave Boundary Layer

- A one-layer time-invariant eddy viscosity model is specified to develop a mathematical model for describing the essential features of the turbulent wave boundary layer over a rough bed. The functional form of the eddy viscosity is evaluated based on computational results from a two-equation turbulence model in which the eddy viscosity varies with time and space. The present eddy viscosity model simplifies much of the mathematical complexity in many existing models. Predictions from the present model have been compared with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.     

Large Eddy Simulation for Wave Breaking in the Surf Zone

In this paper, (he large eddy simulation method is used combined with the marker and cell method to study the wave propagation or shoaling and breaking process. As wave propagates into shallow water, the shoaling leads lo the increase of wave height, and then at a certain position, the wave will be breaking. The breaking wave is a powerful agent for generating turbulence, which plays an important role in most of the fluid dynamic processes throughout the surf zone, such as transformation of wave energy, generation of near-shore current and diffusion of materials. So a proper numerical model for describing the turbulence effect is needed. In this paper, a revised Smagorinsky subgrid-scale mode! is used to describe the turbulence effect. The present study reveals that the coefficient of the Smagorinsky model for wave propagation or breaking simulation may be taken as a varying function of the water depth and distance away from the wave breaking point. The large eddy simulation model presented in this pape     

浅海流体动力学一种含变湍粘性系数的流速分解模型(Ⅱ)——模型在超浅海风暴潮零阶问题中的应用

本文将流速分解模型应用于作为超浅海风暴潮的渤海风潮,并讨论了变湍粘性系数的确定。作为一个初步的,但较为成功的数值试验例子,描述了实际风场作用下的渤海风潮,比较了变湍粘性系数模型与常湍粘性系数模型的计算结果间的差异。     

A note on a theoretical model of oscillatory smooth turbulent boundary layers

An analytical theory which describes the motion in an oscillatory smooth turbulent boundary layer using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the wall. In the outer layer the eddy viscosity is taken as a constant.     

潜堤上破碎波浪传播变形的数值模型及其验证

为模拟潜堤上破碎波浪传播时产生能量的耗散这一特性,在改进的具有四阶色散的Boussinesq水波方程中中入二阶紊动粘性项,建立了考虑波浪破碎的水波数学模型.在非交错网格下建立了有限差分数值模型,并利用三阶Adams-Bash forth格式预报、四阶Adams-Mouton格式校正对数值模型进行求解.通过数值试验,模拟...     

含变涡动系数的超浅海风暴潮模型

超浅海风暴潮模型提出后[2],对渤海风潮,作为超浅海问题,进行了数值研究[1]。其结果的分析和观测资料的比较都表明了该模型有一定的应用价值;故,对超浅海风暴潮模型作进一步的探讨是有一定意义的。尤其因为我国是一个多浅水域和多风暴潮的国家,这种研究就具有更重要的意义。     

基于大涡模拟和局部滤波同化方法的海洋环流模式

结合最小二乘法极值原理,提出了一种基于局部谱展开的滤波同化方法,把测量数据和数值计算过程中出现的高频短波滤掉,并将高度计数据同化到了求解过程中.结果既增加了数值稳定性,又提高了数值模拟的准确性.针对在海洋环流问题中水平的流动性质和垂直的不同的特点,我们还将大涡模拟的思想和直接涡黏的思想分别应用于水平方向和垂直方向,给出的方法是一种适用于海洋环流和浅水环流问题的大涡模拟湍流模式.对热带和北太平洋一年四季非定常季风作用下环流的数值模拟表明,提出的方法非常有效,数值结果与实际相当吻合.     

On a theoretical model of rough turbulent wave boundary layers

An analytical theory which describes the motion in a turbulent wave boundary layer near a rough sea bottom by using a two-layer time invariant eddy viscosity model is presented. The eddy viscosity in the inner layer increases quadratically with the height above the sea bottom. In the outer layer the eddy viscosity is taken as a constant. The mean velocity and shear stress profiles, the bottom shear stress and the bottom friction coefficient are presented, and comparisons are made with experimental results.     

Bottom friction and its effects on periodic long wave propagation

A new set of Boussinesq-type equations describing the free surface evolution and the corresponding depth-integrated horizontal velocity is derived with the bottom boundary layer effects included. Inside the boundary layer the eddy viscosity gradient model is employed to characterize Reynolds stresses and the eddy viscosity is further approximated as a linear function of the distance measured from the seafloor. Boundary-layer velocities are coupled with the irrotational velocity in the core region through boundary conditions. The leading order boundary layer effects on wave propagation appear in the depth-integrated continuity equation to account for the velocity deficit inside the boundary layer. This formulation is different from the conventional approach in which a bottom stress term is inserted in the momentum equation. An iterative scheme is developed to solve the new model equations for the free surface elevation, depth-integrated velocity, the bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity. A numerical example for the evolution of periodic waves propagating in one-dimensional channel is discussed to illustrate the numerical procedure and physics involved. The differences between the conventional approach and the present formulation are discussed in terms of the bottom frictional stress and the free surface profiles.     

渤海垂直湍流混合强度季节变化的数值模拟

渤海为极浅陆架海 ,其中湍流耗散作用显著。将三维斜压陆架海模式 HAMSOM应用于渤海 ,以渤海周边台站每天 4次的常规气象资料作为风和热驱动 ,渤海海峡开边界以 5个主要分潮调和常数计算水位强迫 ,计算了渤海 1982年水文要素和流场变化 ,并用模式以湍的局地平衡理论封闭计算出垂直湍流粘性的时空分布。结果表明 :渤海湍流混合冬强夏弱 ,变化幅度较大 ( 10～ 2 0 0 cm2 / s) ,这是风搅拌和潮混合的湍流输入在密度层化调整下的结果 ;风的作用在冬季强于潮的作用 ,而底层则由潮混合控制呈现半月周期 ;渤海湍粘性系数的空间分布十分复杂 ,这是在渤海地形和岸形轮廓限制下 ,由一定大气条件驱动的流场和密度场导致的湍流混合强度不同所致     

Estimation of eddy viscosity on the South China Sea shelf with adjoint assimilation method

The eddy viscosity of the ocean is an important parameter indicating the small-scale mixing process in the oceanic interior water column.Ekman wind-driven current model and adjoint assimilation technique are used to calculate the vertical profiles of eddy viscosity by fitting model results to the observation data.The data used in the paper include observed wind data and ADCP data obtained at Wenchang Oil Rig on the SCS (the South China Sea) shelf in August 2002.Different simulations under different wind conditions are analyzed to explore how the eddy viscosity develops with varying wind field.The results show that the eddy viscosity endured gradual variations in the range of 10^-3-10^-2 m²/s during the periods of wind changes.The mean eddy viscosity undergoing strong wind could rise by about 25% as compared to the value under weak wind.     

An approximate solution of wave-modified Ekman current for gradually varying eddy viscosity

An approximate steady solution of the wave-modified Ekman current is presented for gradually varying eddy viscosity by using the WKB method with the variation of parameters technique. The parameters involved in the solution can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water. The solution reduces to the exact solution when the eddy viscosity is taken as a constant. As illustrative examples, for a fully developed wind-generated sea with different wind speeds and a few proposed gradually varying eddy viscosities, the current profiles calculated from the approximate solutions are compared with those of the exact solutions or numerical ones by using the Donelan and Pierson wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. It is shown that the approximate solution presented has an elegant form and yet would be valid for any given gradually varying eddy viscosity. The applicability of the solution method to the real ocean is discussed following the comparisons with published observational data and with the results from a large eddy simulation of the Ekman layer.     

FVCOM模型关键参数的处理及其在涌潮模拟中的应用

通过改进海床阻力系数和设置合适的垂向紊动背景系数,应用FVCOM模型成功再现了钱塘江河口强涌潮的演进过程。海床阻力系数采用Manning公式形式,取值随水深、地形在0.000 2~0.002 9之间变化;垂向紊动背景系数取1×10^-4 m²/s。模拟结果较好地复演了涌潮到达时刻、涌潮高度及涌潮抬升过程、涌潮水平流速以及其沿垂向分布规律,表明阻力系数及垂向紊动背景系数等关键参数的改进和处理是合理的,可应用于涌潮三维潮流运动特征模拟。     

A Study of Eddy Viscosity Coefficient in Numerical Tidal Simulation

Based on the fluid motion equations, the physical meaning of eddy viscosity coefficient and the rationality of the Boussinesq hypothesis are discussed in this paper. The effect of the coefficient on numerical stability is analyzed briefly. A semi-enclosed rectangular sea area, with an orthogonal spur dike, is applied in a 2-D numerical model to study the effect of horizontal eddy viscosity coefficient (AH). The computed result shows that AH has little influence on the tidal level and averaged flow velocity, but has obvious influence on the intensity and the range of return flow around near the spur dike. Correspondingly, a wind-driven current pool and an annular current are applied in a 3-D numerical model respectively to study the effect of vertical eddy viscosity coefficient (Av). The computed result shows that the absolute value of Av is inversely proportional to that of horizontal velocity, and the vertical gradient value of Av determines the vertical distribution of horizontal velocity. The distrib     

Energy balance of wind waves as a function of the bottom friction formulation

Four different expressions for wave energy dissipation by bottom friction are intercompared. For this purpose, the SWAN wave model and the wave data set of Lake George (Australia) are used. Three formulations are already present in SWAN (ver. 40.01): the JONSWAP expression, the drag law friction model of Collins and the eddy–viscosity model of Madsen. The eddy–viscosity model of Weber was incorporated into the SWAN code. Using Collins' and Weber's expressions, the depth- and fetch-limited wave growth laws obtained in the nearly idealized situation of Lake George can be reproduced. The wave model has shown the best performance using the formulation of Weber. This formula has some advantages over the other formulations. The expression is based on theoretical and physical principles. The wave height and the peak frequency obtained from the SWAN runs using Weber's bottom friction expression are more consistent with the measurements. The formula of Weber should therefore be preferred when modelling waves in very shallow water.     

A numerical model for wave motions and turbulence flows in front of a composite breakwater

A mathematical model based on the Volume-Averaged/Reynolds Averaged Navier-Stokes (VARANS) equations is developed to describe surface wave motions in the vicinity of a coastal structure, which could be either a rigid solid structure or a permeable structure or a combination of both. In the VARANS equations, the volume-averaged Reynolds stress is modeled by adopting the nonlinear eddy viscosity assumption. The model equations for the volume-averaged turbulent kinetic energy and its dissipation rate are derived by taking the volume-average of the standard k−ϵ equations. Because of the volume-averaging process, the effects of the small-scale turbulence in porous media are introduced. The performance of the model is checked by comparing numerical solutions with the experimental data related to a composite breakwater reported by Sakakiyama and Liu [Coast. Eng. 121 (2001) 117].     

Comparison of turbulence schemes for prediction of wave-induced near-bed sediment suspension above a plane bed

Based on a wave bottom boundary layer model and a sediment advection-diffusion model, seven turbulence schemes are compared regarding their performances in prediction of near-bed sediment suspension beneath waves above a plane bed. These turbulence algorithms include six empirical eddy viscosity schemes and one standard two-equation k-ε model. In particular, different combinations of typical empirical formulas for the eddy viscosity profile and for the wave friction factor are examined. Numerical results are compared with four laboratory data sets, consisting of one wave boundary layer hydrodynamics experiment and three sediment suspension experiments under linear waves and the Stokes second-order waves. It is shown that predictions of near-bed sediment suspension are very sensitive to the choices of the empirical formulas in turbulence schemes. Simple empirical turbulence schemes are possible to perform equally well as the two-equation k-ε model. Among the empirical schemes, the turbulence scheme, combining the exponential formula for eddy viscosity and Swart formula for wave friction factor, is the most accurate. It maintains the simplicity and yields identically good predictions as the k-ε model does in terms of the wave-averaged sediment concentration.     

中尺度涡条件下的深海声场效应研究

通过构建中尺度涡的数学模型,利用射线-简正波-抛物方程(RMPE)声学模型进行传播损失计算,进而分析在深海声道、深海会聚区、海底反射3种传播模式下,中尺度涡对深海声效应的影响。数值仿真结果显示,暖涡对深海声道、会聚区产生下压效果,使会聚区水平距离变大,深海声道深度方向上变宽;冷涡使会聚区上抬,距离变短,对声场散射现象明显。研究结果表明,涡旋环境条件下,声场特征会产生显著变化。试验结果揭示了中尺度涡对深海声场效应的影响,对指导海上运用中尺度涡现象开展的科学研究、工程实践、军事运用具有积极的指导意义。     

On extracting current profiles from vertically integrated numerical models

A transformation method is presented by which current profiles (of tidal or wind-induced origin) can be extracted at any horizontal position and moment in time from a vertically integrated, two-dimensional, hydrodynamic numerical model. An arbitrary vertical variation of eddy viscosity can be included in the method, which can incorporate a no-slip bottom boundary condition. The technique assumes that the sea is homogeneous.The method is used to improve the representation of bottom stress within the two-dimensional model, whereby the bottom stress is no longer related simply to the depth-mean current as in the “conventional” two-dimensional, vertically integrated model.Idealized calculations for a range of eddy viscosity profiles, show that elevations, current profiles, and time series of current extracted from this “enhanced” two-dimensional numerical model are in good agreement with currents obtained from a full three-dimensional model.     

Three-dimensional structure of tidal current in the East China Sea and the Yellow Sea

A three-dimensional tidal current model is developed and applied to the East China Sea (ECS), the Yellow Sea and the Bohai Sea. The model well reproduces the major four tides, namely M₂, S₂, K₁ and O₁ tides, and their currents. The horizontal distributions of the major four tidal currents are the same as those calculated by the horizontal two-dimensional models. With its high resolutions in the horizontal (12.5 km) and the vertical (20 layers), the model is used to investigate the vertical distributions of tidal current. Four vertical eddy viscosity models are used in the numerical experiments. As the tidal current becomes strong, its vertical shear becomes large and its vertical profile becomes sensitive to the vertical eddy viscosity. As a conclusion, the HU (a) model (Davieset al., 1997), which relates the vertical eddy viscosity to the water depth and depth mean velocity, gives the closest results to the observed data. The reproduction of the amphidromic point of M₂ tide in Liaodong Bay is discussed and it is concluded that it depends on the bottom friction stress. The model reproduces a unique vertical profile of tidal current in the Yellow Sea, which is also found in the observed data. The reason for the reproduction of such a unique profile in the model is investigated.