A numerical model of the long term flow along the Malin-Hebrides shelf

A three dimensional hydrodynamic model of the Malin-Hebrides shelf region is used to investigate the spatial variability of the wind and tidally induced residual flow in the region and the influence of flow from the Irish Sea and along the shelf edge. By this means it is possible to understand the spatial variability in the long term observed flow fields in the region and the range of driving forces producing this flow. The model uses a sigma coordinate grid in the vertical with a finer grid in the near surface and near bed shear layers. The vertical diffusion of momentum in the model is parameterised using an eddy viscosity coefficient which is derived from turbulence energy closure models. Two different turbulence models are used to compute the eddy viscosity, namely a two-equation (itq²−q²ℓ) model which has prognostic equations for both turbulence energy and mixing length and a simpler model in which the mixing length is a specified algebraic function of the water depth.The wind induced response to spatially and temporally constant orthogonal wind stresses, namely westerly and southerly winds of 1 N m⁻², are derived from the model. By using orthogonal winds and assuming linearity, then to first order the response to any wind direction can be derived. Computed flows show a uniform wind driven surface layer of magnitude about 3% of the wind speed and direction 15 ° to the right of the wind, in deep water. Currents at depth particularly in the shelf edge and near coastal region show significant spatial variability which is related to variations in bottom topography and the coastline.Calculations show that tidal residual flows are only significant in the near coastal regions where the tidal current is strong and exhibits spatial variability. Flow into the region from the Irish Sea through the North Channel although having its greatest influence in the near coastal region, does affect currents near the shelf edge region. Again the spatial variability of the flow is influenced by topographic effects.A detailed examination of wind induced current profiles together with turbulence, mixing length and viscosity, at a number of locations in the model from deep ocean to shallow near coastal, shows that both turbulence models yield comparable results, with the mixing length in the two equation model showing a similar dependence to that specified in the simpler turbulence model.Calculations clearly show that flow along the shelf edge area to the west of Ireland and from the Irish Sea entering the region, together with local wind forcing can have a major effect upon currents along the Malin-Hebrides shelf. The flow fields show significant spatial variability in the region, comparable to those deduced from long term tracer measurements. The spatial variability found in the calculations suggests that a very intense measurement programme together with inflow measurements into the area is required to understand the circulation in the region, and provide data sets suitable for a rigorous model validation.     

A 3D finite-element model of the Adriatic tides

A 3D finite-element numerical model is applied to the Adriatic Sea to simulate its tidal motions. This fully nonlinear model includes a free surface, very realistic topography, and an advanced turbulence closure. Comparison with available tidal elevations at coastal stations and with tidal ellipses at a few locations in the open sea demonstrates that the model simulations are highly accurate. The results are then used to determine the 3D distribution of the tidal residual currents.     

Spatial variability of the barotropic M2 constituent tidal current over the Rías Baixas Galician shelf (NW Spain)

Using current meters and systematically repeated vessel mounted ADCP data legs, we describe the role of the semidiurnal and diurnal constituents in the tidal currents and investigate the mesoscale variability of the M₂ tidal currents field along three cross-shelf legs over the Galician shelf. We found that the estimated values of the semi-major axes of the main semidiurnal tidal constituents are closely related to those obtained in previous research and that the tidal currents are predominantly semidiurnal. Amplitudes of the M₂ and S₂ semi-major axes constituents are comparable, and important fortnightly variability should thus be expected in the amplitude of the semidiurnal tidal currents. Vertical profiles of the semi-major axes of the main tidal constituents reveal that, in the absence of stratification, and far from the bottom frictional effects, the tidal currents are mostly barotropic. Over the slope, the tidal ellipses tilt from a north–south orientation toward the northeast–southwest direction and, as we go further into the shelf, their amplitude is increased, a feature that is reasonably explained by the transition from the dynamics of a Poincaré wave offshore to the dynamics of a northward alongshore propagating Kelvin wave over the shelf. The Ría de Vigo exerts a notable influence over the tidal currents, acting as an extension of the shelf and introducing a meridional variation in the orientation of the ellipses from the alongshore direction in the southern straight coast toward the northeast–southwest direction at the latitude of the Rías. Finally, the spatial fitting methods we tried have proved to be successful in VMADCP data detiding in this region.     

Numerical simulation of the barotropic tides in the Tunisian Shelf and the Strait of Sicily

We have investigated the barotropic tides in the Tunisian shelf and the Strait of Sicily using the Regional Ocean Modelling System (ROMS) with very high-resolution. Model performance was evaluated with respect to tide gauge, satellite data, and current meter measurements. The model fields faithfully reproduced the major feature of the barotropic tidal currents and agreed well with existing tidal elevation and phase observations. General features for the various semidiurnal constituents are nearly similar to each other with maximum amplitude in the Gulf of Gabes. The larger tidal currents occur over the continental shelves. In the Adventure Bank, the current is essentially of diurnal type whereas in the Gulf of Gabes it is of semidiurnal type.Tidal energy lost, which is primarily due to bottom stress dissipation, is predominantly in the Gulf of Gabes ( 61%), the Strait of Sicily, and the Strait of Messina. The forcing function for internal tides shows for both M₂ and K₁ constituents, significant spatial variability in the Strait of Sicily. This suggests that some internal tides will be generated in these regions and could thus explain the observed strong diurnal internal waves in the Adventure Bank.     

A 3D, finite element model for baroclinic circulation on the Vancouver Island continental shelf

This paper describes the development and application of a 3-dimensional model of the barotropic and baroclinic circulation on the continental shelf west of Vancouver Island, Canada. A previous study with a 2D barotropic model and field data revealed that several tidal constituents have a significant baroclinic component (the K1 in particular). Thus we embarked on another study with a 3D model to study the baroclinic effects on the residual and several selected tidal constituents.The 3D model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for density so that density gradient forcing is included in the momentum equations. However, the study presented here describes diagnostic calculations for the baroclinic residual circulation only.The model is sufficiently efficient that it encourages sensitivity testing with a large number of model runs. In this sense, the model is akin to an extension of analytical solutions to the domain of irregular geometry and bottom topography where this parameter space can be explored in some detail.In particular, the consequences of the sigma coordinate system used by the model are explored. Test cases using an idealized representation of the continental shelf, shelf break and shelf slope, lead to an estimation of the velocity errors caused by interpolation errors inherent in the sigma coordinate system. On the basis of these estimates, the computational grid used in the 2D model is found to have inadequate resolution. Thus a new grid is generated with increased accuracy in the region of the shelf break. However, even with increased resolution, spurious baroclinic circulation seaward of the shelf break and in the vicinity of Juan de Fuca canyon remained a significant problem when the pressure gradient terms were evaluated using the σ coordinate system and using a realistic density profile.With the new grid, diagnostic calculations of the barotropic and baroclinic residual circulation are performed using forcing from the observed σ_t (density) field and from the gradient of this field.     

白令海潮汐能通量和底边界能耗散

The spatial distribution of the energy flux, bottom boundary layer (BBL) energy dissipation, surface elevation amplitude and current magnitude of the major semidiurnal tidal constituents in the Bering Sea are examined in detail. These distributions are obtained from the results of a three-dimensional numerical simulation model (POM). Compared with observation data from seven stations, the root mean square errors of tidal height are 2.6 cm and 1.2 cm for M₂ and N₂ respectively, and those of phase-lag are 21.8° and 15.8° respectively. The majority of the tidal energy flux off the deep basin is along the shelf edge, although some of this flux crosses the shelf edge, especially in the southeast of the shelf break. The total M₂ energy dissipation in the Bering Sea is 30.43 GW, which is about 10 times of that of N₂ and S₂. The semidiurnal tidal energy enters mainly to the Bering Sea by Samalga Pass, Amukta Pass and Seguam Pass, accounting more than 60% of the total energy entering the Being Sea from the Pacific.     

Baroclinic eddy formation in a Rhine plume model

A three-dimensional finite difference tidal model, including advective and diffusive transport of salinity, is used in the two-layer model for simulation of Rhine water outflow. Layer depths are adjusted in a way that no advective transports between upper and lower layer take place in case of sufficiently stable stratification.Model results show frontal eddy development related to (limited) growing internal waves in case of weak northeasterly to southeasterly winds. It is shown that baroclinically unstable conditions occur, related to vertical velocity shear, resulting in frontal meanders with wave lengths between 18 and 30 km. Satellite images of sea surface temperature show a comparable behaviour of the temperature front, which is strongly correlated with the salinity front of the Rhine plume.     

Advection schemes for shelf sea models

Numerical models of shelf seas must handle sharp gradients in thermoclines and fronts, and at the edges of patches of passive tracer, often in the presence of strong tidal currents, without introducing excessive numerical diffusion or spurious oscillations. In a sigma coordinate model there is an additional problem, since then purely horizontal motion over a sloping sea bed may introduce strong numerical diffusion in the vertical, which can artificially erode thermoclines.In this paper, two advection schemes applicable to shelf sea models are examined. They are based on TVD (Total Variation Diminishing) and PPM (Piecewise Parabolic Method) techniques. They are demonstrated to give satisfactory performance for tracer advection in one, two and three dimensions. They are both monotonic, and the PPM scheme has particularly low numerical diffusion. In two and three dimensions directional splitting is used, which is handled by following advection with each horizontal velocity component by adjustment of the sigma levels in each water column using the same advection scheme. The artificial vertical diffusion is then small, particularly with PPM.The two schemes are also compared in a three-dimensional model of a cylindrical eddy of relatively fresh water, released from rest in an open sea region. Here, both salinity and momentum are advected. Laboratory experiments show that after an initial period of adjustment the eddy should become unstable, with a growth of cyclonic-anticyclonic eddy pairs. This is reproduced in the model, with the PPM scheme again producing sharper results than the TVD scheme.Integrated second moment calculations are used to compare the schemes. These demonstrate the lower numerical diffusion of the PPM scheme. This advantage is achieved at the cost of greater computing time.     

黄河三角洲海域的潮汐流动数值模拟

文章将一种有效处理浅水流动计算中的Roe型二阶精度迎风型FVM格式应用到平面二维浅水流动数学模型中.为保证Roe格式的稳定性,应用Ropers格式以解决通量梯度项与源项的平衡问题.为避免源项引起的计算不稳定,对源项采用分步法及半隐式求解.在此基础上,应用该模型对地形复杂的黄河三角洲海域潮汐进行了实际数值模拟.并对其水动...     

河床下切影响下珠江三角洲潮流不对称时空变化规律

潮流不对称对三角洲地区的泥沙净输运和地貌演变有着重要作用,近年来珠江三角洲的大规模采砂活动引起河床大幅下切,因此研究河床下切后珠江三角洲潮流不对称的时空变化规律具有重要意义。利用1999年和2010年珠江三角洲河口河网地形数据,建立珠江口平面二维水动力模型,模拟珠江河口河网枯季水动力过程。结合非稳态调和分析方法分解流速信号,用偏度方法量化分潮组合、余流及分潮和余流相互作用对潮流不对称的贡献程度。研究结果表明:1)珠江三角洲潮流不对称受余流影响呈现出落潮占优的特性;2)河床下切后,各分潮组合的不对称性增大,潮流不对称在下游河道有所减弱、中上游河道有所增强,且珠江三角洲中上游河道变化大于下游河道;3)分潮和余流相互作用的变化是导致该现象产生的主要原因。     

On the residual advection of passive constituents

In this paper, the different approaches used to simulate the long-term advection of passive constituents on tidal shelves are discussed in the framework of large scale hydrodynamic modelling. The direct approach in which the unsteady mesoscale (tides and storm surges) and macroscale (monthly or seasonal mean processes) currents are used is very demanding in computer resources (CPU and memory). On the other hand, the use of residual velocities gives a larger understanding of the long-term transport processes and simplifies numerical treatments. However, the definition of such appropriate velocities is still an open question. In the context of large scale models, Lagrangian residuals are not applicable. Eulerian residual transport velocities fail to represent long-term motions when tidal non-linearities are important. The first order Lagrangian residual velocity introduced by Feng et al. (1986) and generalized here is shown to be a very good solution. The North-Western European Continental Shelf (NWECS) is used as an example to compare the numerical solutions obtained with the different approaches.     

The influence of different turbulence schemes on modelling primary production in a 1D coupled physical–biological model

A one-dimensional (1D) coupled physical–microbiological model has been applied to a site in the central North Sea. The impact of the choice of the turbulence closure scheme on the modelling the primary production has been investigated.The model was run with four different parameterisations of vertical mixing of heat, momentum and dissolved and suspended matters, using M2 tidal forcing and the hourly mean meteorological forcing of 1989 to reproduce the annual thermal structure and primary production. The four mixing parameterisations are: Level 2 turbulence closure scheme [Mellor, G.L., Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806; Mellor, G.L., Yamada, T., 1982. Development of a turbulence closure model for geophysical Fluid problems. Rev. Geophys. Space Phys. 20 (4) 851–875] using an explicit numerical scheme [Sharples, J., Tett, P., 1994. Modelling the effect of physical variability on the midwater chlorophyll maximum. J. Mar. Res. 52, 219–238]; a version of the Level 2.5 turbulence closure scheme [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55–62; Ruddick, K.G., Deleersnijder, E., Luyten, P.J., Ozer, J., 1995. Haline stratification in the rhine/meuse freshwater plume: a 3D model sensitivity analysis. Cont. Shelf Res. 15 (13) 1597–1630] simplified to use an algebraic mixing length by Sharples and Simpson [Sharples, J., Simpson, J.H., 1995. Semidiurnal and longer period stability cycles in the Liverpool Bay region of freshwater influence. Cont. Shelf Res. 15, 295–313], also solved explicitly; the same simplified L2.5 scheme with an implicit numerical solution and modified vertical discretisation scheme [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206]; and another version of the same scheme (but using a different algebraic mixing length) as described by Xing and Davies [Xing, J., Davies, A.M., 1996a. Application of turbulence energy models to the computation of tidal currents and mixing intensities in the shelf edge regions. J. Phys. Oceanogr. 26, 417–447; Xing, J., Davies, A.M., 1996b. Application of a range of turbulence models to the computation of tidal currents and mixing intensities in shelf edge regions. Cont. Shelf. Res. 16, 517–547; Xing, J., Davies, A.M., 1998. Application of a range of turbulence energy models to the computation of the internal tide. Int. J. Numer. Methods Fluids 26, 1055–1084]. Various model outputs at the sea surface and in depth profiles have been compared with data collected in 1989 as part of the North Sea Project [Huthnance, J.M., 1990. Progress on North Sea Project. NERC News, vol. 12, pp. 25–29, UK]. It is shown that the biological results are extremely sensitive to the small changes in the physical conditions, which arise due to the different turbulence schemes tested. The timing of the spring bloom and the maintenance of the midwater chlorophyll maximum all differ greatly between model runs, and the gross primary production varies by a factor of two from the highest to lowest results. The simplified Level 2.5 scheme, implemented using the numerical methods of Annan [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206], produces results, which give the best agreement with the available data.     

The wind-forced response on a buoyant coastal current: Observations of the western Gulf of Maine plume

The freshwater plume in the western Gulf of Maine is being studied as part of an interdisciplinary investigation of the physical transport of a toxic alga. A field program was conducted in the springs of 1993 and 1994 to map the spatial and temporal patterns of salinity, currents and algal toxicity. The observations suggest that the plume's cross-shore structure varies markedly as a function of fluctuations in alongshore wind forcing. Consistent with Ekman drift dynamics, upwelling favorable winds spread the plume offshore, at times widening it to over 50 km in offshore extent, while downwelling favorable winds narrow the plume width to as little as 10 km.Using a simple slab model, we find qualitative agreement between the observed variations of plume width and those predicted by Ekman theory for short time scales of integration. Near surface current meters show significant correlations between cross-shore currents and alongshore wind stress, consistent with Ekman theory. Estimates of the terms in the alongshore momentum equation calculated from moored current meter arrays also indicate a dominant Ekman balance within the plume. A significant correlation between alongshore currents and winds suggests that interfacial drag may be important, although inclusion of a Raleigh drag term does not significantly improve the alongshore momentum balance.     

A three-dimensional, wave-current coupled, sediment transport model for POM

In the high-energy environment of coastal seas and estuaries,strong sediment resuspension/ deposition events are driven by surface waves,tides,winds and buoyancy driven currents.In recent years,A POM based three-dimensional,wave-current coupled,sediment transport model has been developed by the University of New South Wales.This paper presents several examples of the model applications to study sediment dynamics in the environments where forcings such as waves,tides,and winds are equally important to affect sediment fluxes and distributions.Firstly,the sediment transport model coupled to the Yellow Sea general circulation model and a third generation wave model SWAN was implemented in the Yellow Sea to study the dynamics of the sediment transport and resuspension in the northern Jiangsu shoal-wate(rNJSW).The sediment distributions and fluxes and their inter-annual variability were studied by realistic numerical simulations.The study found that the surface waves played a dominant role over the tides to form the turbidity maxima along the muddy coast of NJSW. Secondly,the sediment transport model was used to explore the effect of suspended sediment-induced stratification in the bottom boundary laye(rBBL).The model uses a re-parameterized bottom drag coefficient Cd that incorporates a linear stability function of flux Richardson number Rf.The study has shown that the sediment induced stratification in the BBL reduces the vertical eddy viscosity and bottom shear stress in comparison with the model prediction in a neutrally stratified BBL.In response to these apparent reductions,the tidal current shear is increased and sediments are abnormally concentrated within a thin wall layer that is overlain by a thicker layer with much smaller concentration.The formation of this fluid-mud layer near the seabed has led to a significant reduction in the total sediment transport.This study contributes to the understanding of formations of tidal flats along the coasts of turbid seas and estuaries.     

如东海域西太阳沙人工岛陆岛通道实体堤合理长度潮流数模研究

分析了江苏如东海域烂沙洋南水道的稳定性,建立了基于不规则三角形网格有限差分法的江苏如东海域大范围和小范围嵌套二维潮流数学模型,在对模型验证的基础上,对西太阳沙人工岛工程的陆岛通道实体堤合理长度进行了潮流场数值模拟研究。研究结果表明,烂沙洋南水道主槽基本上是稳定的,从潮流场和烂沙洋南水道的稳定性角度考虑,陆岛通道实体堤合理长度应不超过6 km.     

Circulation on the Armorican shelf (Bay of Biscay) in autumn

Three drifters drogued at 65 m were launched on a transect on the Armorican shelf of the Bay of Biscay for 4 years. The experiments were conducted in autumn. They revealed a north-westward, poleward current over the 100 m isobath and a very weak eastward current over depths comprised between 120 and 150 m. A model was used to assess the role of residual tidal currents and wind-induced circulation. The results show that the former are quite weak and the latter do not explain the average velocity of over 10 cm s^− 1. It is thought that this current is mainly driven by the density gradient induced by the breakdown of stratification. Hydrological data and satellite images from the period are discussed, in the light of this hypothesis.     

The interaction of tidal advection, diffusion and mussel filtration in a tidal channel

Time series measurements of flow and pigment concentrations (Chl) in the Menai Strait have revealed that the strong residual flow in a tidal channel ( 500 m³ s^− 1) transports phytoplankton from the open sea into the channel where much of it is consumed by suspension feeders, mainly in commercial beds of Mytilus edulis. The progressive depletion of phytoplankton along the channel results in a strong horizontal gradient of plankton and hence Chl. Tidal displacement of this gradient causes large (± 50% of mean) oscillations of Chl in the vicinity of the mussel beds. Vertical mixing by the strong tidal flows is sufficiently vigorous for most of the tidal cycle to ensure that downward diffusion can resupply the near-bed layer although there are indications of some transient depletion around slack water.This paradigm of the interaction of advection, diffusion and filtration determining the distribution of plankton and its supply to mussels has been encapsulated in a series of simple models forced only by boundary values. In the first, a 1-D model of tidal flow in the channel reproduces the principal features of the observed currents including the unusually large spatial change in phase of the currents and the variation of the residual transport with tidal range. The flow field from this physical model is used to drive a second model based on the advection diffusion equation for Chl with a source at the Irish Sea boundary and a sink over the mussel bed. This model illustrates the formation of a strong Chl gradient along the channel and simulates the amplitude and phase of the M₂ oscillations of Chl and the development of the M₄ variation apparent in the observations. This second model has been extended to 2-D over the mussel beds to allow investigation of the effects of water column mixing. The model indicates that only for a short period ( 30 min), close to slack water, is mixing sufficiently reduced to permit the development of a depletion boundary layer and then only within  1 m from the bottom, a result which is consistent with the observations.     

A two-layer model of the Rhine plume

The outflow of Rhine water into the shallow Southern Bight of the North Sea leads to almost discontinuous vertical density distributions and sharp frontal structures around the river mouth. Strong tidal motion, wind and baroclinic effects have large influence on the dynamics and dispersion of river water. A three-dimensional tidal model, including advective and diffusive transport of salinity, is used in the two-layer mode for simulation of Rhine water outflow to quantify the interaction of the different processes and the effect on dispersion and mixing of river water. Layer depths are adjusted in a way that no advective transports between upper and lower layer take place in case of sufficiently stable stratification. In case of weak or no stratification the upper layer depth is fixed, and advective transports between layers are computed. Model results show frontal eddy development and (limited) growing internal waves due to baroclinic instability. Comparisons with observational data are presented.     

粉砂淤泥质潮滩对于波浪作用的响应

以江苏中部沿海的开敞型粉砂淤泥质潮滩为原型,建立平面二维潮流、波浪、泥沙输运及地貌演变概化数学模型,研究了潮流、波浪作用下潮滩地貌演变机制,重点分析粉砂淤泥质潮滩对于波浪作用的响应.研究表明,在潮汐作用为主时,潮滩保持淤长的趋势,剖面形态保持双凸形;随着波浪作用的增强,床面冲刷作用增强,淤长型潮滩转变为侵蚀性潮滩,双凸...     

甬江及口外海域潮流泥沙数值模拟

建立了甬江河道及口外海域平面二维潮流泥沙数学模型,对2015年6月半个月的潮流场和悬沙场进行模拟,模拟结果与实测资料吻合良好。计算得到了研究区域洪季的余流场和输沙格局,结果表明:甬江口外余流整体由西北指向东南,河道余流指向下游;除口门局部水域,甬江口外输沙格局基本与余流场一致,悬沙经涨潮流的作用被带入甬江河道,致使河道内近口门处的输沙格局由口门向内;甬江口局部区域输沙格局与余流场存在差异的原因是悬沙输移与潮流运动存在时间上的滞后。