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。     

Two sets of higher-order Boussinesq-type equations for water waves

Based on the classical Boussinesq model by Peregrine [Peregrine, D.H., 1967. Long waves on a beach. J. Fluid Mech. 27 (4), 815–827], two parameters are introduced to improve dispersion and linear shoaling characteristics. The higher order non-linear terms are added to the modified Boussinesq equations. The non-linearity of the Boussinesq model is analyzed. A parameter related to h/L₀ is used to improve the quadratic transfer function in relatively deep water. Since the dispersion characteristic of the modified Boussinesq equations with two parameters is only equal to the second-order Padé expansion of the linear dispersion relation, further improvement is done by introducing a new velocity vector to replace the depth-averaged one in the modified Boussinesq equations. The dispersion characteristic of the further modified Boussinesq equations is accurate to the fourth-order Padé approximation of the linear dispersion relation. Compared to the modified Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling characteristic of the equations has higher accuracy from shallow water to deep water.     

Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field

Based on the 2D horizontal plane numerical model,a quasi-3D numerical model is establishedfor coastal regions of shallow water.The characteristics of this model are that the velocity profiles can be ob-tained at the same time when the equations of the value of difference between the horizontal current velocityand its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent withthe results of the 2D model.The circulating flow in the rectangular area induced by wind is simulated and ap-plied to the tidal flow field of the radial sandbanks in the South Yellow Sea.The computational results fromthis quasi-3D model are in good agreement with analytical results and observed data.The solution of the finitedifference equations has been found to be stable,and the model is simple,effective and practical.     

A Three-Dimensional Nearshore Hydrodynamic Model with Depth-Dependent Radiation Stresses

For the simulation of the three-dimensional (3D) nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-depeedent radiation stresses in the Cartsian coordinates are introduced on the basis of the linear wave theory,and then vertical variations of depth-dependent radiation stresses are discussed.The 3D hydrodynamic model of EICIRC (Eulerian-Lagrangian CIRCulation) is extended by adding the terms of the depth-dependent or depth-averaged radiation stresses in the momentum equations.The wave set-up,set-down and undertow are simulated by the extended ELCIRC model based on the wave fields provided by the experiment or the REF/DIF wave model.The simulated results with the depth-dependent and depth-averaged radiation stresses both show good agreement with the experimental data for wave set-up and set-down.The undertow profiles predicted by the model with the depth-dependent radiation stresses are also consistent with the experimental results,while the model with the depth-averaged radiation stresses can not reflect the vertical distribution of undertow.     

A new form of higher order Boussinesq equations

On the basis of the higher order Boussinesq equations derived by the author (1999), a new form of higher order Boussinesq equations is developed through replacing the depth-averaged velocity vector by a new velocity vector in the equations in order to increase the accuracy of the linear dispersion, shoaling property and nonlinear characteristics of the equations. The dispersion of the new equations is accurate to a [4/4] Pade expansion in kh. Compared to the previous higher order Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling property of the equations have higher accuracy from shallow water to deep water.     

A finite-element,multi-scale model of the Scheldt tributaries,river, estuary and ROFI

We report on the development and validation of a coupled two- and one-dimensional finite-element model for the Scheldt tributaries, river, estuary and region of fresh water influence (ROFI). The hydrodynamic equations are solved on a single, unstructured, multi-scale mesh stretching from the shelf break to the Scheldt tributaries. The tide is forced on the shelf break and propagates upstream in the riverine network. Upstream boundaries lie on sluices or outside of the region of tidal dominance where daily averaged discharges are imposed. Two-dimensional, depth-averaged shallow water equations are solved by means of the discontinuous Galerkin (DG) method over the marine and estuarine parts of the computational domain. In the rivers, however, one-dimensional equations are dealt with using the DG method with the addition of a technique to cope with confluence points. Model parameters are carefully calibrated, leading to the simulation of wind- and tide-forced flows that are in excellent agreement with available data. The diffusivity in the transport equation is calibrated using time series of salinity at various locations in the estuary. Finally, the Lagrangian residual transport in the estuary and the adjacent coastal zone is investigated. This work is a major step towards an integrated model for studying the dynamics of waterborne contaminants and the water renewal timescales in the Scheldt land-sea continuum.     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

Numerical Modeling of Suspended Sediment Transport in the Gulf of Kachchh Including Kandla Creek,West Coast of India

A depth-averaged numerical model has been developed to study tidal circulation and suspended sediment transport in the Gulf of Kachchh including Kandla creek, west coast of India. The resolution of the model is taken as 750 m × 750 m, which is found to be adequate for the gulf region. However, this resolution could not produce the realistic circulation pattern and suspended sediment concentration in the Kandla creek region. There is a major seaport at Kandla which serves as the sea gate to northwest India. Therefore, a 2-D fine resolution (75 m × 75 m) model for Kandla creek has been developed and coupled with the coarser gulf model to compute the flow features in the creek region. The model dynamics and basic formulation remain the same for both the gulf model and the creek model. The models are barotropic, based on shallow water equations, and neglect horizontal diffusion and wind stress terms in the momentum equations. The models are fully nonlinear and use a semiexplicit finite difference scheme to solve mass, momentum, and advection-diffusion equations in a horizontal plane. The tide in the gulf is represented in the model by the semidiurnal M₂ constituent mainly. In this study, no fresh water discharge conditions have been considered so the results are appropriate for the dry season. Numerical experiments are carried out to study the circulation and suspended sediment concentrations in the gulf and the creek regions. The computed results are validated with the available observations.     

Numerical Modeling of Suspended Sediment Transport in the Gulf of Kachchh Including Kandla Creek, West Coast of India

A depth-averaged numerical model has been developed to study tidal circulation and suspended sediment transport in the Gulf of Kachchh including Kandla creek, west coast of India. The resolution of the model is taken as 750 m × 750 m, which is found to be adequate for the gulf region. However, this resolution could not produce the realistic circulation pattern and suspended sediment concentration in the Kandla creek region. There is a major seaport at Kandla which serves as the sea gate to northwest India. Therefore, a 2-D fine resolution (75 m × 75 m) model for Kandla creek has been developed and coupled with the coarser gulf model to compute the flow features in the creek region. The model dynamics and basic formulation remain the same for both the gulf model and the creek model. The models are barotropic, based on shallow water equations, and neglect horizontal diffusion and wind stress terms in the momentum equations. The models are fully nonlinear and use a semiexplicit finite difference scheme to solve mass, momentum, and advection-diffusion equations in a horizontal plane. The tide in the gulf is represented in the model by the semidiurnal M₂ constituent mainly. In this study, no fresh water discharge conditions have been considered so the results are appropriate for the dry season. Numerical experiments are carried out to study the circulation and suspended sediment concentrations in the gulf and the creek regions. The computed results are validated with the available observations.     

Transport of waste heat from a nuclear power plant into coastal water

A numerical and experimental modeling is presented for studying the transport of waste heat from a nuclear power plant into coastal water by using a full-field physical model with scale distortion, a local physical model with normal scale and a depth-averaged k− turbulence model with a modified second-order upwind scheme. Field investigations are also used to provide the calibration and validation of the modeling. A case study simulating the turbulent tidal flow and waste heat transport in the coastal water near Daya Bay Nuclear Power Plant in Southern China was conducted. The experimental result of the case study shows that the water temperature in coastal water was a little oversimulated near the surface and was a little undersimulated near the bottom of heated-water layer by the full-field physical model. The numerical study shows that the depth-averaged k− turbulence model presented a satisfied prediction of turbulent tidal flow and far-field temperature distribution in coastal water, although the near-field stratification due to the heated water effluent was not accounted for. The result of the effect of scale distortion on physical model shows that a full-field physical model with a scale distortion of 10 produced a satisfied result of temperature distribution in the present case study.     

Mass transport in a two-layer wave boundary layer

The transport of a chemical species under the pure action of surface progressive waves in the benthic boundary layer which is loaded with dense suspended sediments is studied theoretically. The flow structure of the boundary layer is approximated by that of a two-layer Stokes boundary layer with a sharp interface between clear water and a heavy fluid. The simplest model of constant eddy diffusivities is adopted and the exchange of matter with the bed is ignored. For a thin layer of heavy fluid, whose thickness is comparable to the surface wave amplitude and the Stokes boundary layer thickness, effective transport equations are deduced using an averaging technique based on the method of homogenization. The effective advection velocity is found to be equal to the depth-averaged mass transport velocity, while the dispersion coefficient can be shown to be positive definite. Explicit expressions for the transport coefficients are obtained as functions of fluid properties and flow kinematics. Physical discussions on their relations are also presented.     

均匀剪切流场中的强非线性波及其色散关系

考虑了剪切流场中强非线性波,唯一的假设是水深与特征波长之比是小量,建立了基于任意水深处速度而不是通常所用的平均速度为速度变量的模型。不仅改进了色散关系,使模型的水深适用范围更大,而且由于整个推导过程对波的振幅没有做任何假设,因而所获得的模型可以用于任何振幅的波。     

剪切流中界面波的二阶Stokes 波解

考虑了均匀剪切流场中强非线性界面波,建立了基于任意水深处速度而不是通常所用的平均速度为速度变量的模型,分析了其色散关系,并求得了各层速度的二阶渐近解和界面内波波面位移的二阶Stokes解,揭示了波流之间的非线性相互作用和界面波解之间的非线性相互作用。     

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

Filtering inertia-gravity waves from the initial conditions of the linear shallow water equations

A method for filtering inertia-gravity waves from elevation and depth-averaged velocity is described. This filtering scheme is derived from the linear shallow water equations for constant depth and constant Coriolis frequency. The filtered solution is obtained by retaining only the eigenvectors corresponding to the geostrophic equilibrium and by discarding explicitly the eigenvectors corresponding to the fast moving inertia-gravity waves. An alternative formulation is derived using a variational approach. Both filtering methods are tested numerically for a periodic domain with constant depth and the variational approach is implemented for a closed domain with large topographic variations. The filtering methods significantly reduce the amplitudes of the inertia-gravity waves while preserving the mean flow. The variational method is compared to the Incremental Analysis Update technique and the benefits of the variational filter are presented.     

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

Numerical study on the flow characteristics of tidal jets induced by a tidal-jet-generator

The flow characteristics of tidal jets induced by a Tidal-Jet Generator (TJG) are investigated using a finite-difference numerical scheme, named Navier–Stokes (NS)–Marker and Cell (MAC)-TIDE, based on the fully 3D NS equations. The TJG is an enclosed rectangular breakwater, which has vertical opening and a large enclosed volume inside. During both phases of tide, strong and uni-directional jets can be obtained locally from the inlet of the TJG, due to the water level difference between the inner and outer sides of TJG.The computed results are extensively compared with three other independently developed numerical models; 3D-ADI, DVM, and CIP-CSF. These models are based on quasi-3D, 2D depth-averaged, and fully 3D NS equations, respectively. It is seen that the present fully 3D numerical model NS–MAC-TIDE can predict the maximum intensity of inlet velocity with higher accuracy than the other numerical models when compared with the empirical function proposed from the experiments. The numerical simulations based on NS–MAC-TIDE can reproduce successfully the processes of generation, development, and dissipation of tidal jets. The effects of gap opening on the main characteristics of the tidal jet flow are assessed. Through numerical assessment, it is also clearly demonstrated that the residual time of a pollutant distributed around the front of the TJG can be decreased by significant amount due to the locally induced tidal jet. The TJG can thus utilize tidal energy for water purification in local marine environment by providing a flushing mechanism.     

Laboratory and numerical study of dambreak-generated swash on impermeable slopes

New laboratory experiments have produced detailed measurements of hydrodynamics within swash generated by bore collapse on a steep beach. The experiments are based on a dambreak rig producing a highly repeatable, large-scale swash event, enabling detailed measurements of depths and velocities at a number of locations across the swash zone. Experiments were conducted on two beaches, differentiated by roughness. Results are presented for uprush shoreline motion, flow depths, depth-averaged velocity, velocity profiles and turbulence intensity. Estimates of the time- and spatially-varying bed shear stress are obtained via log-law fitting to the velocity profiles and are compared with the shear plate measurements of Barnes et al. (2009) for similar experimental conditions. Experimental results are compared with model predictions based on a NLSWE model with momentum loss parameterised using the simple quadratic stress law in terms of the depth-averaged velocity. Predicted and measured flow depths and depth-averaged velocities agree reasonably well for much of the swash period, but agreement is not good at the time of bore arrival and towards the end of the backwash. The parameterisation of total momentum loss via the quadratic stress law cannot adequately model the swash bed shear stress at these critical times.     

Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa’s results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa’s (1999) results, and the applicable scope of water depth is deeper.