A 2D Mathematical Model for Sediment Transport by Waves and Tidal Currents

In this study, the combined actions of waves and tidal currents in estuarine and coastal areas are considered and a 2D mathematical model for sediment transport by waves and tidal currents has been established in orthogonal curvilinear coordinates. Non-equilibrium transport equations of suspended load and bed load are used in the model. The concept of background concentration is introduced, and the formula of sediment transport capacity of tidal currents for the Oujiang River estuary is obtained. The Dou Guoren formula is employed for the sediment transport capacity of waves. Sediment transport capacity in the form of mud and the intensity of back silting are calculated by use of Luo Zaosen＇ s formula. The calculated tidal stages are in good agreement with the field data, and the calculated velocities and flow directions of 46 vertical lines for 8 cross sections are also in good agreement with the measured data. On such a basis, simulations of back silting after excavation of the waterway with a sand bar under complicated boundary conditions in the navigation channel induced by suspended load, bed load and mud by waves and tidal currents are discussed.

Surface tidal currents in the open sea area to the east of the Zhoushan Islands measured with high frequency surface wave radar

Based on the quasi-harmonic analysis of 11 d vector ocean currents obtained from two high frequency sur- face wave radars located at Zhujiajian Island and Shengshan Island, the spatial distribution characteristics of surface tidal currents in the open sea area to the east of the Zhoushan Islands of Zhejiang Province, China are studied. The following conclusions are drawn from the analysis： the tidal current pattern in the open sea area to the east of Zhoushan Islands is primarily regular semidiurnal, which is significantly affected by the shallow water constituents. The directions of the major axes of tidal current ellipses of M2 lie approx- imately in the NW-SE direction. With the increasing of distance away from the coast, the directions of the tidal current ellipses gradually shift toward the E-W direction. The tidal currents are mainly reversing cur- rents. The spatial distribution of probable maximum current velocities decreases gradually from northeast to southwest which is basically in accordance with the spatial distribution of measured maximum current velocities. The residual currents near the coast are larger than those far away from the coast. The directions of the residual currents are basically north by east, and the angle to the due north increases gradually with the increasing distance away from the coast. The topography shows a certain impact on the spatial distri- bution of shallow water constituents, the rotation of tidal currents, the probable maximum currents and the residual currents.

Effects of Tidal Currents on Nonlinear Internal Solitary Waves in the South China Sea

The propagation and fission process of internal solitary waves （ISWs） with amplitudes of about 170 m are simulated in the northeast of the South China Sea （NSCS） by using the generalized Korteweg-de Vries （KdV） equation under continuous stratification. More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs. This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current. It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however, there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons （defined as the distance between two neighboring peaks of ISWs）. The difference in nonlinearity coefficient a between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.

Effect of Distortion Ratio on Local Scour Under Tidal Currents and Waves

Five generalized physical models of different distortion ratios were built according to DOU Guo-ren's similarity theory of total sediment transport modeling for estuarine and coastal regions. Experiments on local scour in front of groins were made under the actions of tidal currents and waves with clear and sediment entraining water. The scour depths under different dynamic actions are compared. The effect of the distortion ratio on the depth of scour hole is discussed. A relationship between scour depths for distorted and undistorted models is given.

Numerical simulation of sediment lifted by waves and transported by tidal currents

The analysis of the scabed processes of a muddy coast has been described in this paper. On the basisof the basic differential equation of tidal current and sediment movement influenced by waves, a numerical simulation system for sediment lifted by waves and transported by tidal currents and scabed processes has been established by using MADI method, and applied to the sea area of Tianjin Port with good results.

Wave Scattering by Double Slotted Barriers in A Steady Current:Experiments

The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.

Analysis of Tidal Current Energy Potential in the Major Channels of the Bohai Strait Based on Delft3D

The utilization and development of tidal current energy can help alleviate the current energy shortage,improve the global ecological environment,and maintain sustainable development.In this study,numerical simulation is carried out on a rectangular grid using Delft3D.The tidal current energy potential of the major channels in the Bohai Strait is further simulated and estimated by comparing the simulated and measured data.Results show that the flow module in Delft3D has good modeling ability for the assessment of tidal current energy potential.The average flow velocity,maximum flow velocity,and energy flow density are consistent.The Laotieshan Channel,located in the northern part of the Bohai Strait,shows a large tidal current energy potential.The maximum flow velocity of this channel can reach 2 m s-1,and the maximum energy flow density can exceed 500 W m-2.The tidal current energy in the Laotieshan Channel is more than 10 times that in other channels.Therefore,this study advocates for the continued exploration and exploitation of the tidal current energy resources in the Laotieshan Channel.

Effects of counter-current driven by electron cyclotron waves on neoclassical tearing mode suppression

Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.

Wave Attenuation and Turbulence Driven by Submerged Vegetation Under Current-Wave Flow

A set of laboratory experiments are carried out to investigate the effect of following/opposing currents on wave attenuation.Rigid vegetation canopies with aligned and staggered configurations were tested under the condition of various regular wave heights and current velocities,with the constant water depth being 0.60 m to create the desired submerged scenarios.Results show that the vegetation-induced wave dissipation is enhanced with the increasing incident wave height.A larger velocity magnititude leads to a greater wave height attenuation for both following and opposing current conditions.Moreover,there is a strong positive linear correlation between the damping coefficientβand the relative wave height H_(0)/h,especially for pure wave conditions.For the velocity profile,the distributions of U_(min)and U_(max)show different patterns under combined wave and current.The time-averaged turbulent kinetic energy(TKE)vary little under pure wave and U_(c)=±0.05 m/s conditions.With the increase of flow velocity amplitude,the time-averaged TKE shows a particularly pronounced increase trend at the top of the canopy.The vegetation drag coefficients are obtained by a calibration approach.The empirical relations of drag coefficient with Reynolds and Keulegane-Carpenter numbers are proposed to further understand the wave-current-vegetation interaction mechanism.

Harmonic Energy Transfer for Extreme Waves in Current

Ning et al. （2015） developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and focal position were given. As its extension, harmonic energy transfer for focused waves in uniform current is studied using the proposed model by Ning et al. （2015） and Fast Fourier Transformation （FFT） technique in this study. It shows that the strong opposing currents, inducing partial wave blocking and reducing the extreme wave crest, make the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide an explanation to address the shifts of focal points in consideration of the combination effects of wave nonlinearity and current.

Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography

A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.

Effect of oceanic current on typhoon-wave modeling in the East China Sea

We use the WAVEWATCH-III model to quantify the effect of oceanic current on typhoon-wave modeling in the East-China-Sea（ECS）.Typhoons Jelawat and Saomai in the autumn of 2000 are hindcasted.The oceanic currents in the ECS are mainly constituted of Kuroshio and typhoon-generated currents.The results show distinguishable differences in wave height and wave period under the typhoon conditions.The oceanic current causes the maximum differences,of up to a 0.5 m significant wave height and a 1 s mean wave period.Comparisons between typhoons Jelawat and Saomai show the dependence of the current effect on the typhoon characteristics.

Three-Dimensional Wave-Induced Current Model Equations and Radiation Stresses

After the approach by Mellor （2003, 2008）, the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor （2008）, is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor （2003, 2008）, pointed out by Ardhuin et al. （2008） and Bennis and Ardhuin （2011）, are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. （2008）, the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy’s wave theory and the approach of Mellor （2003, 2008） are applicable for the derivation of the wave-induced current model.

A Linear Theory for Wave Scattering by Double Slotted Barriers in Weak Steady Currents

Recent experimental results have shown that the presence of a steady current can significantly reduce the energy of transmitted waves. In this paper, a theory is developed to study the wave scattering by single or double vertical slotted barriers in the presence of a weak uniform current. The quasi-linear theory is based on an eigenfunction expansion method. Comparisons between theory and existing experimental results for both single slotted barrier and double slotted barriers show satisfactory agreements. In consideration of wave propagation in a weak current it is found that the friction factor used to characterize the head loss at the slotted barrier depends on both the geometry of the slotted barrier and the strength of the steady current.

A study of impact of the reclamation and artificial island projects on tidal currents and sediment concentration in radial sand ridge field of the South Yellow Sea

The two-dimensional hydrodynamic model, MIKE21, is applied to simulate the tidal currents and sediment concentration in the radial sand ridges of the South Yellow Sea. Results are in accordance with in situ observations. Then the variations of tidal currents and suspended sediment concentration caused by reclamation and artificial islands projects are simulated. The results show that the impacts are limited around the project areas. After the projects, the fan-shaped, Jianggang centered tidal current pattern would be replaced by a pattern which is formed by two tidal paths. One locates at the Xiyang channel in north-south direction, and the other locates at the Huangshayang channel in east-west direction. The reclamation of Tiaozini separates the waters into south portion and north portion. The changes of sediment concentrations coincide with those of currents. Both the sediment concentrations and tidal currents increase at the northwest of Dongsha and the south of Gaoni, while both decrease at the north and south of Tiaozini, and the east and southwest of Dongsha.

Refraction-Diffraction Model for Irregular Wave and Directional Spectrum Considering Current

A mild-slope equation for combined refraction and diffraction of random waves in the independent time current is derived using Kirby equation(1984). In the derivation, the frequency of random waves is represented based on the time series concept, by a typical frequency and its deviation part. Numerical results, compared with those of laboratory experiments, demonstrate that new set of irregular mild slope equation with current is of good adaptability.

Research on Current Situation,Symptoms and Protection Technological Measures of Ancient Trees in Surging Waves Pavilion,China

The paper had studied growth situation and disease symptoms of ancient trees in Surging Waves Pavilion.There were 14 ancient trees belonging to 10 genera of 9 families,with tree age of 120-260 years.These trees had been well protected generally.There were 9 ancient trees growing well,occupying 64.29%,which were Ginkgo biloba,Cupressus funebris Endl.,Podocarpus macrophyllus,Zelkova schneideriana Hand.-Mazz,Cinnamomum camphora(L.)Presl,Buxus sinica,and Wisteria sinensis(Sims)Sweet.There were 5 ancient trees needing to be protected preferentially,occupying 35.71%,including Ligustrum lucidum,Osmanthus fragrans and Pterocarya stenoptera.The disease symptoms were trunk rot and hollow structure.Based on these symptoms,the paper had proposed protective measures for Ligustrum lucidum and Osmanthus fragrans:① enclosing eroding holes on the trunk;② clearing up eroded woodiness on the surface of trunk,disinfecting and applying anti-corrosion protectants;③ filling eroded holes of the trunk.Protective measures for Pterocarya stenoptera included:① clearing up the inner part and interior walls;② disinfecting the inside and interior walls of holes;③ applying anti-corrosion protectants.

Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point. The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direc- tion. The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress. An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy. The wave driver model is a phase-averaged wave model based on the wave action balance equation. Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach am used to evaluate the model＇s performance. The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.

Experimental and Numerical Study of Wave-Induced Long-Shore Currents on A Mild Slope Beach

The long-shore current distribution on a mild slope beach is studied by combining the numerical model and the physical experiment. The experiments of long-shore currents under the action of regular and irregular waves are conducted on mild beaches with different slopes in a wave basin. A numerical model is established, which includes a wave propagation model, a wave breaking model and a long-shore current model. The validity of the numerical model is proved by the comparison of its results with the results of the experimental model. It is concluded that the wave-ioduced long-shore current is influenced significantly by the incident wave height, the wave angle and the beach slope. Its application to the Bohai Bay indicates that the wave-induced currents have the same order of magnitude as the tide currents in the near-shore zone of mill slope beach. In the design of wastewater ouffall locations on a mild-slope beach with shallow water of the Bohai Bay, the position of the outfall should be 10 km away from the shoreline, which is outside of the surf-zone.

Numerical modeling of tidal current of LNG terminal in Caofeidian,Bohai Sea

In order to reasonably simulate tidal currents around small structures such as piles in a large-scale model domain, a 2-D hydrodynamic integrated model for Bohai Sea is established with the finite element method. The grid can be discretionarily refined as a non-structure triangle or quadrilateral so that piers can be treated as one or several impermeable elements with an area of 20 to 30 km^2 in a model domain over 85 700 km^2. The computational results of tidal levels and horizontal velocities are in good agreement with the field data. Based on the computed results by the model, the layout of an open 105 DWT liquefied natural gas （LNG）terminal in Caofeidian, Bohal Sea is effectively and reasonably optimized. It can be concluded that the model is suitable and reasonable for direct simulation of tidal currents around small structures in projects.