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.     

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.     

Wave boundary layers in rough turbulent flow

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 a modified one-equation turbulence model in which the eddy viscosity varies in 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 favorably with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.     

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.     

Eddy viscosities and velocities in combined wave-current flows

The eddy viscosities for the steady and the periodic components of combined wave-current flows have been studied quantitatively from the presently available experimental data. It has been found that inside the boundary interaction layer [z < δ] the eddy viscosity ε_c for the steady flow is increased in the presence of waves while outside the boundary interaction layer [z >δ] it is affected little by the wave motion, and that the eddy viscosity ε_w for the wave motion in the boundary layer is independent of the current strength U^*. On the other hand, a new eddy viscosity model is presented to give a good prediction of the velocity distributions of the waves and currents in comparison with experimental data.     

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.     

Bed friction and dissipation in a combined current and wave motion

Two simple two-layer eddy viscosity models, which facilitate analytical solutions, are presented in order to describe the velocity field and associated shear stress in a combined current wave motion. The models, which have the same eddy viscosity in the current boundary layer, but different eddy viscosities in the wave boundary layer, cover together the whole rough turbulent regime. Straightforward definitions are made for the wave friction factor and the current friction factor for the combined motion, which are in accordance with the results for pure waves and pure currents. In this way one avoids the fictitious reference velocities and elliptic integrals which e.g. Grant and Madsen (1978, 1979) experienced. The two friction factors turn out to be functions of four dimensionless parameters. A detailed calculation procedure is presented. Comparison with laboratory experiments yields promising results. A new relation connecting dissipation and bed shear stress is also developed.     

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.     

Modeling of the eddy viscosity by breaking waves

Breaking wave induced nearsurface turbulence has important consequences for many physical and biochemical processes including water column and nutrients mixing,heat and gases exchange across air-sea interface.The energy loss from wave breaking and the bubble plume penetration depth are estimated.As a consequence,the vertical distribution of the turbulent kinetic energy(TKE),the TKE dissipation rate and the eddy viscosity induced by wave breaking are also provided.It is indicated that model results are found to be consistent with the observational evidence that most TKE generated by wave breaking is lost within a depth of a few meters near the sea surface.High turbulence level with intensities of eddy viscosity induced by breaking is nearly four orders larger than υwl(=κuwz),the value predicted for the wall layer scaling close to the surface,where uw is the friction velocity in water,κ with 0.4 is the von Kármán constant,and z is the water depth,and the strength of the eddy viscosity depends both on wind speed and sea state,and decays rapidly through the depth.This leads to the conclusion that the breaking wave induced vertical mixing is mainly limited to the near surface layer,well above the classical values expected from the similarity theory.Deeper down,however,the effects of wave breaking on the vertical mixing become less important.     

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。     

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 three-dimensional multi-level turbulence model for tidal motion

A three-dimensional multi-level turbulence model is developed to simulate tide induced circulation in coastal waters. Based on the bathymetry data, the coastal waters are divided into a number of layers. In every layer, the velocities are integrated along the layer depth. The eddy viscosity and diffusivity are computed from the Prandtl mixing length turbulence model. This multi-level model solves for the water surface elevations and currents in different water depths. Comparison of numerical results with the measured data shows good conformity.     

空间变化的涡粘系数对线性Munk边界层解的影响(英文)

基于Ｐｅｄｌｏｓｋｙ（１９８７）的线性Ｍｕｃｋ边界层模型,引入一随纬向空间变化的侧摩擦系数ＡＨ（ｘ）,以探讨该参数对西边界流的强化结构的影响。结果发现,在风应力和内区解保持不变的情况下,适中线性变化的ＡＨ（ｘ）会使西边界层内的向北急流和其靠内区一侧的逆流均得到加强。文中还给出摩擦应力、相对涡度及平均动能向涡动能的转化率在西边界层内的分布情况。     

一种三次多项式湍黏性底边界层的流场分布

本文通过假定底边界层湍黏性的三次多项式参数化形式,基于简化的Navier–Stokes方程,并利用超几何方程的性质,推导出了湍流粗糙底边界层的速度解析解。同时,得到了底边界层内其他的动力参数,如底剪应力、Ekman传输、Ekman抽吸及近底部速度分布场,从理论上讨论了均匀混合底边界层特征量分布特征。通过数值结果分析,进一步得出底边界层的总速度、亏损速度及其剪应力受平均流的角频率和地球自转影响比较大;而底边界层的动力结构对于底边界层顶部粗糙度不敏感。该涡黏性模式从理论上丰富了底边界层涡黏性的形式,为底边界层的动力系统研究提供了借鉴和理论参考。     

数据同化反演风应力拖曳系数以及垂向涡动黏性系数的分布

所作的孪生实验表明:通过利用变分优化控制技术将气象学和海洋学(表层和次表层)的观测资料同化到海洋的埃克曼层模型中,可将未知的边界条件(风应力拖曳系数)和垂向涡动黏性系数的分布同时反演出来.     

Formulation of a continuously stratified sea model with three-dimensional representation of the upper layer

A two-layered model is considered in which the upper layer is continuously stratified and the lower layer is homogeneous. The system is driven by atmospheric forces. Bottom stress and topography are included in the model. The linear three-dimensional hydrodynamical equations are used to describe the system. Taking the eddy viscosity in the upper layer as inversely proportional to the static stability, the dependent variables are expanded in terms of continuous functions in the vertical (eigenfunctions). Using this method it is possible to compute currents and internal displacements at any depth in the upper layer. The three-dimensional structure of the lower layer is not considered in this model. The equations describing the lower layer are integrated over depth to give depth mean currents. Using a staggered finite-difference grid in the horizontal and a forward time-stepping procedure, numerical test experiments are carried out for a cross section and for a closed rectangular basin.     

AN ESTIMATION OF TURBULENCE STRESSES IN TIDAL CURRENTS OF HANGZHOU BAY

Based on the momentum equations, the turbulence stresses and eddy viscosities along five sections in Hangzhou Bay are estimated by using the observed data of tidal currents and tides. The coefficient of bottom stresses obtained from the calculation is 0.67 × 10-3 on the average and the vertical profiles of the amplitudes of turbulence stresses are almost linear and slight concave downwards, and the phases are deferred continuously from sea-bed. The coefficient of vertical eddy viscosity reaches its maximum at the layer below the mid-depth with a value of about 60 cm2S-I on the average.     

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     

Contributions to the dynamics of the Antarctic Circumpolar Current (A. C. C.) II. Integral relationship

Non-dimensional equations of motion are derived for the A.C.C. of the barotropic mode, including the bottom friction and the horizontal eddy viscosity. Integration of the vorticity equation along a streamline leads to the zeroth order stream function which is dependent only on depth divided by Coriolis parameter. Integration of the momentum equation along a streamline yields the relation between the momentum input by wind stress and its dissipation by the bottom friction and by the horizontal eddy viscosity. This relation determines the magnitude of the stream function. It explains differences in the total transport of the A.C.C. obtained byBryan andCox (1972), though it gives only one third of the total transport obtained byKamenkovich (1972) with his vertical eddy viscosity of 10²cm² s^?1. With 1 cm² s^?1 of this viscosity,Bryan andCox obtained the transport of about 650 or less than 32×10⁶m³s^?1 for constant or variable depth models, respectively. The higher transport is mainly due to broadening of the width of the A.C.C., whereas the lower value is due to its narrowing and meandering which in turn make the horizontal eddy viscosity more effective (by exercising friction on both sides of the A.C.C.) and the wind stress input smaller than the almost zonal streamlines for constant depth. In the Appendix dynamics of the bottom boundary layer is treated to give rational estimates of the bottom stress in terms of the geostrophic flow and is compared to the recent observations of the benthic boundary current in the Straits of Florida and off San Diego.     

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。