SENSITIVITY STUDY OF THE EFFECTS OF WAVE-INDUCED VERTICAL MIXING ON VERTICAL EXCHANGE PROCESSES

The hydrodynamic model COHERENS-SED, developed by the present authors through introducing wave-enhanced bottom stress, wave dependent surface drag coefficient, wave-induced surface mixing, SWAN to COHERENS, is modified to account for wave-induced vertical mixing. The COHERENS-SED model can also be used for one-dimensional, two-dimensional, three-dimensional current and salinity calculations. One-dimensional model and three-dimensional model are used to study the effects of the wave-induced vertical mixing. The horizontal current velocity profiles obtained by the model are in good agreement with the analytical velocity profiles under the same input conditions. Numerical results show that higher wave height would generally generate larger vertical eddy viscosity and lower horizontal velocity. The results for fresh water in Yellow River Delta show that the wave-induced vertical mixing increases the momentum of fresh water transferring ability downwards to seabed and salt water's mixing with upper fresh water. Fresh water flume length is compressed considerably.     

BOTTOM SHEAR STRESS UNDER WAVE-CURRENT INTERACTION

The present work adopts the COHERENS-SWAN model developed by the first author through coupling three-dimensional hydrodynamic model （COHERENS） and third-generation wave model （SWAN）. Inside the COHERENS-SWAN, the SWAN is regarded as a subroutine and the time- and space-varying current velocity and surface elevation are obtained from the COHERENS. Wave-enhanced bottom shear stress, wave induced surface mixing length and wave dependent surface drag coefficient have been introduced into the COHERENS. Secondly, as wave-enhanced bottom shear stress （＂bottom shear stress＂ described as BSS sometimes in this article） is concerned, a modified bottom shear stress Grant and Madsen model which introduces random wave field is given and introduced to COHERENS-SWAN. COHERENS-SWAN is also adopted to simulate three-dimensional flow in the Yellow River Delta with wave-current co-existing. Four numerical experiments were given to study the effects of wave-current interaction on enhancing bottom shear stress. The simulated current velocities, wave height and wave period match well with field measurement data. The simulated significant wave height and wave period for the case with considering the effects of current can give better agreement with measurement data than the case without involving the effects of current. The introduction of random wave generates lower the bottom shear stress than the case without introducing it. There are obvious differences between bottom shear stress of two way interaction and one way interaction. Velocity field obtained by the COHERENS-SWAN is reasonable according to previous studies and measurements.     

Numerical simulation of irregular wave transformation due to wave-induced current

In order to investigate the effects of wave breaking-induced currents on the transformation of irregular waves over a shoal, two numerical model systems, a combination of SWAN plus SHORECIRC and a combination of REF/DIF S plus SHORECIRC, were constructed. The experimental results of irregular breaking waves conducted by Vincent and Briggs [1989, Refraction–diffraction of irregular waves over a mound. J. Waterway Port Coast. Ocean Eng. 115(2), 269-284.] were simulated using these two wave and current model combinations. Even though the two model combinations show a slight disagreement on the wave transformations, the numerical results indicate that it is necessary to take into account the effect of the breaking-induced currents when the waves are breaking over a shoal: The computed results agree much better with the experimental measurements than the simulation results obtained by neglecting the wave-current interaction.     

Three-dimensional unstructured modelling of wave-induced circulation over a plane and irregular beach

Nearshore currents have a complicated circulation structure over a beach due to the mutual interaction between waves and currents. To investigate the wave-induced circulation over a beach, a three-dimensional unstructured model accounting for the combined actions of waves and currents is established. The wave distribution over the beach is computed by a wave model and the depth-dependent wave radiation stresses with the surface roller are employed in the hydrodynamic model. The present model takes the mixing coefficients and the bottom shear stress under waves and currents into account. To evaluate the three-dimensional unstructured model, the laboratory experiments over a plane and irregular beach are used to test the performance of the model. The undertow over a plane beach is well reproduced and the vertical variability is captured. The performance of the model over an irregular beach is well displayed in the reproduction of pairs of counter-rotating primary circulations at the embayment troughs. Meanwhile, the secondary circulations are observed in the swash zone. The model captures the circulation systems over a beach and the circulation structures of the wave-induced currents are well exhibited.     

沙坝海岸上裂流的数值模拟

建立了基于二阶完全非线性Boussinesq水波方程的二维波浪破碎数值模型,对沙坝海岸上产生的裂流进行了数值模拟研究。首先将文献[1]中给出的一组二阶完全非线性Boussinesq方程进行扩展,在动量方程中引入紊动粘性项模拟波浪破碎引起的能量耗散,采用窄逢法处理海岸动边界问题,并考虑了混合子网格效应以及水底摩擦。然后,在矩形网格上离散控制方程,采用有限差分方法和混合四阶Adams-Bashforth-Moulton预报矫正格式建立了数值模型。应用所建立模型对一带沟槽沙坝海岸上产生裂流的实验进行数值模拟,将计算的波高、增减水、时均流速、时均流场等与实验数据进行了比较。数值结果与实验结果吻合较好,这说明建立的数值模型是准确有效的,为下一步应用该模型模拟实际海岸上的裂流提供了研究基础。     

波浪潮流共同作用下长兴岛海区二维悬沙输运数值模拟研究

根据近岸地区波浪、潮流与泥沙运动的规律,把波浪运动概化为在潮周期中具有时均意义的波浪流分布场,将波浪辐射应力以及波流底部剪切应力耦合到潮流运动方程和悬沙输运方程中,建立了非结构网格下近岸波浪和潮流共同作用下的二维悬沙输运数值模型。时间离散采用欧拉向前格式,空间离散采用有限体积法的显式格式。将模型应用于矩形海湾实验和大连长兴岛附近海区悬沙冲淤过程的实际算例。结果表明:波浪对潮位影响很小,但是对近岸流速有较为明显的影响;波流共同作用对近岸泥沙浓度影响比单纯考虑潮流作用可提高40%～100%的幅度。     

Application of SWAN+ADCIRC to tide-surge and wave simulation in Gulf of Maine during Patriot's Day storm

The southern coast of the Gulf of Maine in the United States is prone to flooding caused by nor'easters. A state-of-the-art fully-coupled model, the Simulating WAves Nearshore(SWAN) model with unstructured grids and the ADvanced CIRCulation(ADCIRC) model, was used to study the hydrodynamic response in the Gulf of Maine during the Patriot's Day storm of 2007, a notable example of nor'easters in this area. The model predictions agree well with the observed tide-surges and waves during this storm event. Waves and circulation in the Gulf of Maine were analyzed. The Georges Bank plays an important role in dissipating wave energy through the bottom friction when waves propagate over the bank from offshore to the inner gulf due to its shallow bathymetry. Wave energy dissipation results in decreasing significant wave height(SWH) in the cross-bank direction and wave radiation stress gradient, which in turn induces changes in currents. While the tidal currents are dominant over the Georges Bank and in the Bay of Fundy, the residual currents generated by the meteorological forcing and waves are significant over the Georges Bank and in the coastal area and can reach 0.3 m/s and 0.2 m/s, respectively. In the vicinity of the coast, the longshore current generated by the surface wind stress and wave radiation stress acting parallel to the coastline is inversely proportional to the water depth and will eventually be limited by the bottom friction. The storm surge level reaches 0.8 m along the western periphery of the Gulf of Maine while the wave set-up due to radiation stress variation reaches 0.2 m. Therefore, it is significant to coastal flooding.     

波-流共同作用下令仃洋三维盐度数值模拟

为了研究伶仃洋内盐度的输移运动规律,建立了三维斜压盐度数学模型。模型考虑了径流、潮流及波浪场作用下的盐度输运,波浪的影响通过三维辐射应力和波一流共同作用底应力反映。采用平面正交曲线坐标和垂向σ坐标对复杂边界和地形进行了较好的拟合,方程采用守恒有限差分法离散,并采用内外模式分裂技术求解,水平动量方程的求解采用了“预测”、“校正”相结合的方法以保证内外模式所求流速值的一致性。应用枯水期伶仃洋大规模同期实测的水位、流速和盐度资料对模型进行了验证,计算值与实测值吻合较好,表明了模型对伶仃洋水流、盐度运动规律模拟的可靠性。     

THREE-DIMENSIONAL NUMERICAL MODELLING OF THE WAVE-IN- DUCED RIP CURRENTS UNDER IRREGULAR BATHYMETRY

A process-based 3-D hydrodynamic model is established to simulate the rip current structures under irregular bathymetry.The depth-varying wave-induced residual momentum,the surface rollers,the turbulent mixing and the wave-current interactions are considered.Experimental datasets are used to validate the model,and it is shown that the model can effectively describe the 3-D structures of the rip currents in both normal and oblique wave incident cases.The flow patterns of the rip currents see various characteristics for different incident wave directions.In the normal incident case,pairs of counter-rotating primary circulation cells are formed,and an offshore rip flow occurs in the embayment troughs.The peak seaward velocities occur at the top of the bed boundary layer,and the undertow is incorporated in addition to the rip currents.In the oblique incident case,the longshore currents are dominant,which result in a meandering flow along the depth contour,and the undertow is weaker compared to that in the normal incident condition.     

Process control of the sand wave migration in Beibu Gulf of the South China Sea

Based on the environment characteristics of the Beibu Gulf of South China Sea, a quasi-three-dimensional physical model is built.By coupling the bottom boundary layer with the two-dimensional tidal current field near the seabed surface, the quasi-three-dimensional hydrodynamic numerical simulation is carried out.The sand wave migration process is dealt with by coupling the hydrodynamic model with the sediment transport model.The computational results are shown to be in good agreement with the observed data,...     

Impacts of wind waves on sediment transport in a large,shallow lake

Lake Okeechobee is a large, shallow subtropical lake, located in south Florida. Over the last several decades, Lake Okeechobee has experienced accelerated eutrophication due to excessive phosphorus loads from agricultural run‐off. Recycling of phosphorus from bottom sediments through resuspension is critical to addressing eutrophication of the lake and for water quality management. The present study investigates the impacts of wind waves on sediment transport in Lake Okeechobee, using measured data and the Lake Okeechobee Environmental Model (LOEM). The LOEM was fully calibrated and verified with more than 10 years of measured data in previous studies. Analysis of the measured data indicates significant wave height (SWH) and suspended sediment concentration are closely correlated to the wind speed in the lake. The nonlinear interaction of high‐frequency wind waves with relatively low‐frequency currents in the boundary layer plays a key role in sediment deposition/resuspension. Without considering the effects of wind waves, the bottom shear stress can be greatly underestimated. The spatial variations of key variables for sediment modelling, including SWH, water depth, orbital velocity, current velocity, bottom shear stress and sediment concentration, are discussed. In general, the near‐bottom wave velocity (and the associated bottom shear stress) is greater than or the same order of magnitude as the near‐bed current velocity (and the associated bottom shear stress) in this shallow water system. Although the sediment zones of Lake Okeechobee were described in previous studies, few published papers discussed its formation mechanisms. The findings of the present study include that the multiyear averaged bottom shear stress with wind‐wave effect plays a key role in forming the spatial patterns of the sediment zones. The study results are currently being used in lake management and in developing strategies for reducing phosphorus in the lake.     

风拖曳力系数和曼宁系数对风暴潮流模拟的影响

利用0205号威马逊台风期间实测风暴增水和风暴潮流数据,采用NCEP FNL和台风模型风场的融合风场作为驱动项,建立了覆盖东海的三维风暴潮流数值模型,研究风拖曳力系数和曼宁系数对风暴增水和风暴潮流的影响。计算结果表明:(1)风拖曳力系数取值应考虑随风速变化。表层风暴潮流受风拖曳力系数影响较大,中层和底层风暴潮流基本不受影响。(2)风暴潮流结构在一定程度上取决于曼宁系数;曼宁系数对中层和底层风暴潮流影响大于表层,曼宁系数越大,底摩擦阻力越大,风暴潮流垂向分层越明显。(3)风暴增水和风暴潮流对曼宁系数的响应不同,建立模型时,应同时率定风暴增水和风暴潮流。     

基于有限体积法的三维波生近岸流数值模型

波浪破碎产生近岸流是近岸浅水区域一个重要的水动力现象。该文利用辐射应力的概念,并考虑辐射应力沿水深的变化、波浪破碎引起的水滚以及波流共同作用下的水底剪应力,建立了基于有限体积法的三维波生近岸流数值模型。运用建立的数值模型模拟了两个实验室实验,并同实验的实测结果进行了对比。结果表明,建立的数值模型能够较好地模拟波浪破碎产生的近岸流。     

AN EXPERIMENTAL STUDY ON EFFECTS OF THE BETA TOPOGRAPHY ON SURFACE FLOWS IN A ROTATING ANNULUS SUBJECT TO RADIAL TEMPERATURE GRADIENT

1.INTRODUCTIONLaboratory experi ments for rotating and strat-ified flows play ani mportant role in understandingthe large-scale effects in the Earth’s at mosphereand ocean[1-2].It is known that the beta effect,ortheβ-effect,is of great significance for many fowphenomena in geophysical fluid,such as the Leewaves due to large-scale topography and thewestwardintensification in the ocean[3].The longwave inthe at mosphereis generally regarded as theRossby wave,but a disputed opinion[4]was p…     

INTERACTION BETWEEN WAVES,STRUCTURES AND SAND BEDS

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NUMERICAL SIMULATION OF WAVE-INDUCED CURRENT WITH VERTICALLY VARIED RADIATION STRESS

This article analyzes the vertical structure of the onshore current including the wave-induced current by an equation developed for the radiation stress against water depth. A coupled model COHERENS-SED is adopted to calculate the wave, tidal current, wave-induced current and sediment simultaneously. By applying the new model to Yangpu Bay, its reliability is verified. Then an ideal coastal domain is defined to simulate the nearshore current and wave setup with normal incident waves. The numerical and experimental results for the vertical structure show two undertows, also a visible setup in the surf zone. It demonstrates the importance of the radiation stress in wave-induced currents and mean water levels (set-up/down).     

UNSTEADY WAVES DUE TO AN IMPULSIVE OSEENLET BENEATH THE CAPILLARY SURFACE OF A VISCOUS FLUID

The two-dimensional free-surface waves due to a point force steadily moving beneath the capillary surface of an incompressible viscous fluid of infinite depth were analytically investigated. The unsteady Oseen equations were taken as the governing equations for the viscous flows. The kinematic and dynamic conditions including the combined effects of surface tension and viscosity were linearized for small-amplitude waves on the free-surface. The point force is modeled as an impulsive Oseenlet. The complex dispersion relation for the capillary-gravity waves shows that the wave patterns are characterized by the Weber number and the Reynolds number. The asymptotic expansions for the wave profiles were explicitly derived by means of Lighthill’s theorem for the Fourier transform of a function with a finite number of singularities. Furthermore, it is found that the unsteady wave system consists of four families, that is, the steady-state gravity wave, the steady-state capillary wave, the transient gravity wave, and the transient capillary wave. The effect of viscosity on the capillary-gravity was analytically expressed.     

太湖湖流、波浪、沉积物的三维数值模拟

运用ECOMSED模拟风速为6.5 m/s定常东南风作用下太湖流场及波浪场,对模型的适用性及可靠性进行验证;在此基础上进行波流共同作用下沉积物再悬浮数值模拟,得出沉积物-水界面切应力及水体中悬浮物浓度分布。结果表明:太湖有效波高范围在9~29 cm之间,有效波高的空间分布与风速、风向和水深有很大的关系,同时波浪对切应力会产生很大影响,而切应力的分布决定了悬浮物浓度的分布,风浪及地形要素是导致太湖悬浮物浓度变化的重要因子。模拟结果与现有实验成果较吻合,说明运用该模型模拟太湖沉积物再悬浮的结果可靠。     

COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL

1. INTRODUCTIONWave transformation,one of the most i mpor-tant near-shore hydrodynamic processes , has closerelations to human activities as well as i mpact on o-ceanic environment , resources and engineeringstructures .So it is of greater i mportance to …     

Sources and scales of near-bottom turbulent mixing in large meromictic Lake Iseo

Mixing dynamics in the bottom boundary layer (BBL) of lakes is of primary importance for mediating mass and heat fluxes across the upper sediment. In lakes with depth of several hundred meters, the BBL mixing is often suggested to be low; however, quantitative information from these depths is extremely rare. We assessed the mixing conditions in the BBL of Lake Iseo, a 256 m deep, meromictic Italian lake, where anoxia and accumulation of phosphorus is a major issue. High-resolution temperature and currents measurements demonstrated regular development of turbulence at 220 m depth, with dissipation rates of the turbulent kinetic energy up to 10⁻⁷ W kg⁻¹, characteristic of a shear boundary layer. Analysis of temperature and oxygen dynamics revealed a direct link between the turbulence intensification in the BBL and the passage of a 90-h period basin-scale internal wave. This slow oscillatory motion was attributed to lake-wide internal waves of second vertical mode, whose effect in the upper part of the water column was much less profound. The wave passages were able to increase hypolimnetic velocities above 1 cm s⁻¹, to produce thermal instability across the BBL and to significantly enhance turbulent mixing in the deepest waters. During periods of high velocity bursts, the chemical stratification in the BBL was effectively eroded while direct sediment resuspension was unlikely. The new results reveal the turbulent character of the bottom boundary mixing in deep lakes, highlighting the direct link to wind-driven motions and important effects on the water–sediment exchange of solutes.