Numerical experiment on the computation of the equatorial circulation on the basis of a conservative model

A finite-difference system of motion equations for a baroclinic ocean with an irregular bottom is developed on the basis of the box method and the method of indefinite coefficients. The numerical model is shown to possess the property of conserving momentum, mass, and energy. In the case of barotropic motion, the finite-difference scheme retains potential enstrophy. A numerical experiment on the adaptation of hydrophysical fields in the Equatorial Atlantic in summer was carried out within the framework of the model developed. We managed to obtain a series of features of the equatorial circulation when the coefficients of turbulent exchange and diffusion were small enough.Translated by Mikhail M. Trufanov.     

特征线计算格式下共轭方程两种导出途径的比较

共轭方程的导出是建立资料同化模型的关键，其导出方式有两种途径：AFD形式与FDA形式。在特征线计算格式基础上针对一类较广泛海洋动力控制方程分析了其两种共轭方程（AFD形式与FDA形式）之间的关系，并将理论结果应用于波谱共轭方程的讨论。     

沿岸海域三维斜压场的数值模拟 Ⅱ、渤海湍流能量数值计算

研究建立渤海海域三维斜压场的湍流能量模型。对计算网格无法分辩的湍流运动，引入湍流能量求得垂向动量、质量及能量交换系统，从而形成封闭的湍流运动方程组。定量地计算了湍流能量、湍流速度及有风、无风状况下湍流能量的垂直分布等，探讨了湍流运动对潮波运动的影响。     

潮汐水域中污水侧向排放的数值模拟

基于N-S方程,采用深度平均的应力-通量代数全场模型,模拟流场及热水或污染物侧向排入大水体的各向异性的输移扩散规律。模型中采用深度平均的连续、动量、浓度方程进行潮汐流动的数值模拟计算,潮流采用非对称潮流,模拟结果给出了一个周期内流场、污染物浓度场随时间的变化特征。所得的数值结果与他人的模型实验结果非常一致,而较其他结果更合理,说明本模型的合理性和可靠性。     

A Three-Dimensional Prediction Method for Thermal Diffusion

A three-dimensional,first order turbulence closure,thermal diffusion model is described inthis paper.The governing equations consist of an equation of continuity,three components of momentum,conservation equations for salt,temperature and subgridscale energy,and an equation of state.In the mod-el,according to the hypothesis of Kolmogorov and Prandtl,the viscosity coefficient of turbulent flow ofhomogeneous fluid is related to the local turbulent energy,and the horizontal and vertical exchangecoefficients of mass,heat and momentum are computed with the introduction of subgridscale turbulenceenergy.The governing equations are solved by finite difference techniques.This model is applied to theJiaozhou bay to predict thermal pollution by the Huangdao power plant.An instantaneous tidal currentfield is computed,then the distribution of temperature increment is predicted,and finally the effect of windstress on thermal discharge is discussed.     

A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth

A formal derivation of the improved Boussinesq equations of Madsen and Sørens (1992) is presented to provide the correct forms of the depth-gradient related terms. Linear shoaling characteristics of the new equations are investigated by the method of Madsen and Sørensen (1992) and by the energy flux concept separately and found to agree perfectly, whereas these approaches give conflicting results for the equations derived by Madsen and Sørensen (1992). Furthermore, Nwogu's (1993) modified Boussinesq model is found to produce a linear shoaling-gradient identical with the present work. Numerical modelling of the derived equations for directional waves is carried out by three-time-level finite-difference approximations. A higher-order radiation condition is implemented for effective absorption of the outgoing waves. Several test cases are included to demonstrate the performance of the model.     

C.C. Mei, The applied dynamics of ocean surface waves, Wiley, New York (1983) xvii + 740 pp., £ stg. 66.75.

A theoretical model is developed for wave heights and set-up in a surf zone. In the time-averaged equations of energy and momentum the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the effect of the surface roller in the breaker and the actual shape of the waves. To the first approximation the roller represents a volume of water moving with the wave speed. It significantly changes both energy flux and radiation stress of the surf zone waves. The equations of energy and momentum are solved simultaneously to give the wave height variation and the set-up. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analyzed and shown to be in accordance with the above-mentioned ideas and results.     

Wave heights and set-up in a surf zone

A theoretical model is developed for wave heights and set-up in a surf zone. In the time-averaged equations of energy and momentum the energy flux, radiation stress and energy dissipation are determined by simple approximations which include the effect of the surface roller in the breaker and the actual shape of the waves. To the first approximation the roller represents a volume of water moving with the wave speed. It significantly changes both energy flux and radiation stress of the surf zone waves. The equations of energy and momentum are solved simultaneously to give the wave height variation and the set-up. Comparison with measurements shows good agreement. Also the transitions immediately after breaking are analyzed and shown to be in accordance with the above-mentioned ideas and results.     

Investigation of the sensitivity of the Mellor–Yamada parametrization to the choice of finite-difference analogs in a numerical three-dimensional model of the operative prediction of currents in the black sea

Within the framework of the Mellor–Yamada approach, we realize a numerical scheme for the calculation of the coefficients of turbulent viscosity and diffusion in the z -system of coordinates for the three-dimensional model of operative prediction of currents in the Black Sea. Some discrete analogs of the equations for turbulent kinetic energy and turbulence macroscale are studied. Their high sensitivity to the choice of finite-difference approximations is demonstrated. On the basis of the comparison of the results of prognostic experiments with the data of observations, we choose the best approximation of the term used to describe the generation pf turbulence energy.     

Yangtze Brackish water plume—circulation and diffusion

A system of 3-D linearized momentum equations, the continuity equation and a simplified equation of state for sea water are analytically solved. The solution comprises three parts. The first part is a wind-driven current, the second a jet-like current caused by Yangtze River outflow and the last a density flow. The computed current velocity is obtained by solving an advection-diffusion equation of salinity by a finite-difference method. The results show that the Yangtze brackish water plume spreads as a large low salinity tongue. At the surface, the turning of the tongue axis is mainly controlled by wind stress, Yangtze run-off and bottom topography. Near the bottom, the axis changes little all the year around. At about 10–15 m depth, there is a sharp halocline in summer, but at deeper layers the vertical distribution is almost always uniform. The computed salinity distribution agrees fairly well with the observed one.     

Numerical modeling of gas hydrate emplacements in oceanic sediments

We have implemented a 2-dimensional numerical model for simulating gas hydrate and free gas accumulation in marine sediments. The starting equations are those of the conservation of the transport of momentum, energy, and mass, as well as those of the thermodynamics of methane hydrate stability and methane solubility in the pore-fluid. These constitutive equations are then integrated into a finite element in space, finite-difference in time scheme. We are then able to examine the formation and distribution of methane hydrate and free gas in a simple geologic framework, with respect to the geothermal heat flow, fluid flow, the methane in-situ production and basal flux. Three simulations are performed, leading to the build up of hydrate emplacements largely linear through time. Models act primarily as free gas accumulators and are relatively inefficient with respect to hydrate emplacements: 26–33% of formed methane are converted to hydrate. Seepage of methane across the sea-floor is negligible for fluid flow below 2. 10⁻¹¹ kg/m²/s. At 5.625 10⁻¹¹ kg/m²/s however, 9.7% of the formed methane seeps out of the model. Moreover, along strike variation arising in the 2-dimensional model are outlined. In the absence of focused flow, the thermodynamics of hydrate accumulation are primarily one-dimensional. However, changes in free methane compressibility (density) and methane solubility (the intrinsic dissolved methane flux) subtlety impact on the formation of a free gas zone and the distribution of the hydrate emplacements in our 2-dimensional simulations.     

Numerical modeling of gas hydrate emplacements in oceanic sediments

We have implemented a 2-dimensional numerical model for simulating gas hydrate and free gas accumulation in marine sediments. The starting equations are those of the conservation of the transport of momentum, energy, and mass, as well as those of the thermodynamics of methane hydrate stability and methane solubility in the pore-fluid. These constitutive equations are then integrated into a finite element in space, finite-difference in time scheme. We are then able to examine the formation and distribution of methane hydrate and free gas in a simple geologic framework, with respect to the geothermal heat flow, fluid flow, the methane in-situ production and basal flux. Three simulations are performed, leading to the build up of hydrate emplacements largely linear through time. Models act primarily as free gas accumulators and are relatively inefficient with respect to hydrate emplacements: 26–33% of formed methane are converted to hydrate. Seepage of methane across the sea-floor is negligible for fluid flow below 2. 10⁻¹¹ kg/m²/s. At 5.625 10⁻¹¹ kg/m²/s however, 9.7% of the formed methane seeps out of the model. Moreover, along strike variation arising in the 2-dimensional model are outlined. In the absence of focused flow, the thermodynamics of hydrate accumulation are primarily one-dimensional. However, changes in free methane compressibility (density) and methane solubility (the intrinsic dissolved methane flux) subtlety impact on the formation of a free gas zone and the distribution of the hydrate emplacements in our 2-dimensional simulations.     

热带气旋下海浪对大气向海洋输入的动量和能量的影响

海浪不仅决定着海洋表面的粗糙度,由热带气旋引起的海浪,还通过其发展演化控制着大部分的海气之间的动量和能量传递。本文采用热带气旋观测数据IBTrACS和海浪模式WW III的模拟结果探究了热带气旋下海浪对大气向海洋输入的动量和能量的影响。结果发现,近30 a热带气旋的强度约每10 a增加 1 m/s,但移速没有明显变化。热带气旋的强度越大,从大气输入到海浪和从海浪输入到海流中的动量之差和能量之差也越大。由于热带气旋的风场和海浪场都有较强的不对称性,海气动量差和能量差也表现出非均匀分布:动量差较大的区域在热带气旋移动方向的后方,能量差的最大值则分布在右后象限,且二者均为左前方比较小。逆波龄与动量差和能量差呈高度正相关,相关系数约为0.95,说明波越年轻吸收的动量和能量越多。气旋移速越快逆波龄越大,且热带气旋移动速度与动量差和能量差呈正相关,相关系数在0.8以上。因此,海浪影响着大气向海洋输入的动量和能量的分布和大小,在以后关于海洋边界动力学和热力学的研究中,考虑海浪的演化可能会使结果更加准确。     

Cross-Frontal Water Exchange on Georges Bank: Some Results from an U.S. GLOBEC/Georges Bank Program Model Study

This paper reviews recent progress on modeling cross-frontal water exchange on Georges Bank undertaken as part of the U.S. Global Ecosystem Northwest Atlantic/Georges Bank Study (U.S. GLOBEC/Georges Bank Program). A simple conceptual model is described first, followed by a discussion of four physical mechanisms associated with (1) strong nonlinear interaction, (2) asymmetric tidal mixing, (3) varying wind forcing, and (4) chaotic mixing. Some critical issues in modeling studies of fronts are also addressed. A new unstructured grid, finite-volume coastal ocean ecosystem model is introduced. This model combines the best of the finite-difference method for the simplest discrete computational efficiency and the finite-element method for geometric flexibility. Because the finite-volume method discretizes the integral form of the governing equations, this approach provides a better representation for the conservation laws of mass and momentum are satisfied, which is particularly important in the frontal regions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Interaction of waves with non-colinear currents

The present paper reports on a study of the interaction of a current-free monochromatic surface wave field with a wave-free uniform current field in a three-dimensional flow frame. The wave and the current fields are not necessarily collinear with each other. The formulation of the wave-current field is done under the assumption of irrotational and inviscid flow. We have developed the three dimensional expressions describing the characteristics of the combined flow in terms of mass, momentum and energy transport conservation. These equations are found efficient to describe the sought-for combined wave-current field. The parameters describing the wave-current field after the interaction are the surface disturbance amplitude and length, mean water depth, mean current-like parameter and direction of the combined flow, which would be calculated from a set of equations that satisfy conservation of mean mass, momentum and energy flux and a dispersion relation on the free surface before and after the interaction. The results are shown in terms of relative changes in wave heights and lengths, current-like parameters and final directions obtained for the combined wave-current field with respect to current-free wave and wave-free current pre-interaction parameters.     

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。     

中尺度地形扰动的非线性问题半解析解

将大气和海洋中f-平面上中尺度地形的扰动问题统一起来作为一个地球物理流体力学问题，应用涡度、能量和经圈动量守恒条件，将原来高度非线性方程变成一个二阶椭园型非线性方程，用数值模拟方法分析了大气中的过山运动和海洋中的沿岸上升流，给出了与观测接近的模拟结果以及运动过程对内部物理参数和外界条件的敏感性分析。所提方法可供进一步的动力学分析和数值研究参考。     

Numerical model and calculation of the water circulation in the north-western Black Sea

A multilevel model based on primitive equations and a monotonic finite-difference scheme is applied to study the fluid dynamics over the north-western Black Sea shelf. Wind-generated currents and currents induced by river discharge are simulated in terms of the barotropic version. The effects of the bottom topography, the rigid-lid approximation, and the interaction of wind and river discharge-induced flows are examined.Translated by Vladimir A. Puchkin.     

Numerical Simulation of Nonlinear Three Dimensional Waves in Water of Arbitrary Varying Topography

—The numerical simulation is based on the authors＇high-order models with a dissipative termfor nonlinear and dispersive wave in water of varying depth.Corresponding finite-difference equations andgeneral conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phaseshift are also given in this paper.The systematical tests of numerical simulation show that the theoreticalmodels,the finite-difference algorithms and the boundary conditions can give good calculation results forthe wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.