Depth-integrated Model Research Articles

SATELLITE REMOTE SENSING FOR OCEANIC PRIMARY PRODUCTIVITY

Based on the introduction of optical properties and the classification for ocean water, the fundamental principles of satellite measuring oceanic primary productivity (OPP) were illuminated and the processes of atmospheric correction were discussed in detail in this paper; in addition, some extant oceanic primary productivity models were reviewed completely. At present, many scientists are engaged in the research on satellite remote sensing for OPP, and most OPP models are based on chlorophyll. Firstly, these models are discussed by classifying via given some specific examples. These productivity models are often delineated into empirical, semi-analytical, and analytical models; they can also be classified into wavelength-resolved models (WRMs), wavelength-integrated models (WIMs), time-integrated models (TIMs) and depth-integrated models (DIMs) based upon the implicit levels of integration. Meanwhile, some problems relevant to the application of these models have also been discussed.

Modelling trace metal concentration distributions in estuarine waters

Details are given of a numerical model study of the fate and transport of trace metals in estuarine waters, with particular application to the Mersey Estuary, located along the northwest coast of England. A dynamically integrated model was first developed, including a two-dimensional depth-integrated model and a one-dimensional cross-sectional averaged model. This model was then refined to predict the hydrodynamic and sediment and trace metal transport processes in the Mersey Estuary. Details are given of the development of a governing equation of the total trace metal transport, including both dissolved and particulate metals. The model was first calibrated against field data, collected during spring and neap tidal cycles, for water levels, salinity and suspended sediment. The calibrated model was then used to investigate the trace metal transport processes in the Mersey Estuary, with the partition coefficient between the dissolved and adsorbed particulate phases being modelled as a function of salinity. Comparisons were also made between the model predictions and field-measured data along the estuary. Reasonable agreement between the model results and field data has been obtained, indicating that the novel approach to model metal concentration distributions is capable of representing the fate and transport of trace metals in estuarine environments and can be used as computer-based tool for the environment management of estuarine waters.

Modelling sediment transport using a lightweight bed material

Details are given of a combined physical and numerical model study of sediment transport processes in a square harbour caused by tidal motion. The effects on bed level changes due to tidal currents and the configuration of the harbour entrance were investigated. A lightweight material called Cation Resin was used in this study to represent bed sediments in the laboratory experiments. This material enabled the erosion and deposition processes to be exaggerated within the model harbour, in which the magnitude of the flow velocities was relatively small. An unstructured mesh generation technique, namely a quad-tree grid, was incorporated into an existing two-dimensional depth-integrated numerical model to predict the transport of water quality constituents and sediment particle fluxes. The numerical model was further refined to include the prediction of bed level changes. Detailed comparisons between the numerical model predictions and the laboratory data were undertaken. It was found that the numerical model predictions and the laboratory measurements were in good agreement. It was also concluded that Cation Resin was an appropriate material to use for physical modelling of sediment transport processes in laboratory model studies.

Influences of the fish-mouth project and the groins on the flow and sediment ratio of the Yangtze River waterway

A depth-integrated two-dimensional numerical model of current, salinity and sediment transport was proposed and calibrated by the observation data in the Yangtze River Estuary. It was then applied to investigate the flow and sediment ratio of the navigation channel, i.e. the North Channel of the Yangtze River Estuary, before and after the first phase waterway project is implemented. Particularly, the influences of groin length and the orientation of the submerged dam on the flow ratio and sediment load discharging into the North Channel were discussed. The numerical results demonstrate that less sediment load discharges into the navigation channel, which unburdens the waterway dredging, but in the meantime the flow ratio is also decreased. The flow and sediment ratio can be adjusted by changing layout and dimensions of the hydro-structures, such as the groin length, the top height, etc. The effect of the orientation of the submerged dam is more obvious than the groin length.

Simple Approximation to Bottom Friction for Bingham Fluid Depth Integrated Models

Catastrophic gravity driven flows such as debris flows, mud flows, and flow slides cause major economic damage and loss of human life. Numerical models are important prediction tools which can help to design contention, channeling, and routing structures. Their accuracy is limited by that of the rheological model they implement. Bingham models provide a reasonable good compromise between accuracy and simplicity, and they have been frequently used to describe the rheology of hyperconcentrated flows, mudflows, and debris flows. Their use in depth integrated models presents a difficulty. In order to obtain the bottom friction term, one has to obtain the roots of a third order polynomial. This paper describes a depth integrated model for flows of Bingham fluids. Bottom friction is obtained using an approximation which provides good accuracy and saves 20% of CPU time.

Dynamique non linéaire des vagues en zone de surf interne

ABSTRACT In this paper we present a depth-integrated mathematical model for computing the non-linear transformation of waves in the inner surf zone. First, we analyse wave distortion and dissipation processes from the hyperbolic theory for shock wave. Then, we present a comparison between experimental results by Cox [COX 95] and our numerical simulations, which shows the ability of our numerical model to describe the wave dynamics in the inner surf zone.

Application of CFD modelling to study the hydrodynamics of various anaerobic pond configurations

The simulation of hydrodynamics and transport phenomena in waste stabilization ponds is a developing tool worth studying in order to understand their internal processes and interactions. Pond design involves several physical, hydrological, geometric and dynamic variables so as to provide high hydrodynamic efficiency and maximum substrate utilization rates. CFD modelling allows the combination of these factors to predict the behaviour of ponds having different configurations. The two-dimensional depth-integrated model MIKE 21 was used in this study to simulate hydrodynamic and advection-dispersion processes in a full-scale anaerobic pond (AP) located in southwest Colombia. A set of 12 configurations including sludge contents, inlet-outlet positioning, baffling and pond geometry were modelled. Results showed that a crosswise (diagonally opposite) inlet-outlet layout, a length-to-breadth ratio of 2:1, plus provision of two cross baffles at 1/3 L and 2/3 L were the most effective measures to improve overall AP hydrodynamics and dispersion patterns.

Numerical Simulation of Rain Scavenging on Large Release of Water-Soluble Gases

A depth-integrated numerical model GP_Rain was developed to calculate the behavior of neutrally buoyant, highly soluble gases subjected to scavenging by rain. A neutrally buoyant release of hydrogen fluoride is used to illustrate the use of the model. The GP_Rain model was developed in two steps. The part without rain scavenging is based on AFTOX, a Gaussian puff/plume model. Then a first-order decay term for rain scavenging, which was developed by assuming a homogeneous rain field, was added to the concentration calculation for the puff. The model can predict the maximum release distance for a certain concentration limitation and a two-dimensional plume with or without rain.

Modelling tailings dams and mine waste dumps failures

This paper presents a depth-integrated model that can be used to simulate the flowslides, mudflows and debris flows that are caused by the failure of tailing dams, mining waste dumps and other similar structures. The sliding mass is first determined using a coupled elastoplastic finite element code and a suitable constitutive equation. Once failure has been triggered, propagation of the mobilised material is analysed considering flow properties averaged over depth. A simple law of pore pressure dissipation is postulated for cases in which the consolidation and propagation times are of the same order of magnitude.

Wave propagation modeling in coastal engineering

In this paper we review various numerical models for calculating wave propagations from deep water to surf zone, including wave breaking. The limitations and the approximations for each model are briefly discussed. The main focus of the discussions is on the unified depth-integrated model, which can describe fully nonlinear and weakly dispersive waves, and the Reynolds Averaged Navier-Stokes equations model, which can calculate breaking waves and associated turbulence. Several applications of various models are also presented.

A two-dimensional, depth-integrated model for internal wave propagation over variable bathymetry

Based on assumptions of an inviscid fluid and weakly rotational flow, a set of depth-averaged governing equations are developed to model long internal waves in two horizontal dimensions. These waves are assumed to be weakly nonlinear and weakly dispersive, existing in a two-layer system with a small density difference between the layers. No restriction is placed on the bathymetry or the dominant wave propagation direction. A high-order, finite difference numerical algorithm is developed, formally accurate to (Δ x) 4 in space and (Δ t) 4 in time. The model is checked with known analytical solutions and experimental data. Real bathymetry case studies are also performed, including simulations of internal waves evolving in the Strait of Gibraltar and near the island of Dongsha in the China Sea. Numerical results show strong similarities to satellite images taken over the same locations.

Linear Refraction-Diffraction Model for Steep Bathymetry

This paper describes the mathematical formulation, the numerical solution, and the validation of a linear refraction-diffraction model for steep bathymetry. The model involves two coupled governing equations derived from, respectively, the exact seabed boundary condition and the Laplace equation. It reduces to the extended and the original mild-slope model, when the seabed slope is small. Although the present approach is based on depth-integration of flow characteristics, it correctly accounts for the vertical component of the seabed fluid velocity. The formulation is based on the weighted-residual method, and the hybrid element solution is derived from a Galerkin approach. The capability of the present model to simulate flow velocity and wave amplitude over three-dimensional bedforms is examined in a parametric study. The computed results are compared with the original and extended mild-slope solutions and verified with those of a three-dimensional wave model. The present depth-integrated model has the same data requirements as other two-dimensional models, but provides accurate three-dimensional results with only a fraction of the CPU time that would be required by a three-dimensional model.

Role of fine-grained sediment in turbidity current flow dynamics and resulting deposits

A numerical model of a turbidity current driven by poorly-sorted sediment is developed. The model is applied to study the role that finer fractions of suspended sediment play in the evolution of a submarine fan due to the flow of a subsiding turbidity current. The depth-integrated model can treat multiple size fractions of suspended sediment, ranging from clay to coarse sand. The model is implemented in a sensitivity study by varying inflow fractions of suspended sediments. Computed results clearly indicate that a modest increase in fine sediment content in the inflow dramatically increases the sand carrying capacity of a turbidity current. It is also found that clay is more effective than fine or coarse silt in maintaining the momentum and the identity of a current. Downstream fining and gradual thinning of the simulated deposit is observed in computations performed with multiple grain sizes.

Barotropic wind-driven circulation patterns in a closed rectangular basin of variable depth influenced by a peninsula or an island

Abstract. We study how a coastal obstruction (peninsula or coastal island) affects the three-dimensional barotropic currents in an oblong rectangular basin with variable bathymetry across the basin width. The transverse depth profile is asymmetric and the peninsula or island lies in the middle of the long side of the rectangle. A semi-spectral model for the Boussinesq-approximated shallow water equations, developed in Haidvogel et al. and altered for semi-implicit numerical integration in time in Wang and Hutter, is used to find the steady barotropic state circulation pattern to external winds. The structural (qualitative) rearrangements and quanti2tative features of the current pattern are studied under four principal wind directions and different lengths of the peninsula and its inclination relative to the shore. The essentially non-linear relationships of the water flux between the two sub-basins (formed by the obstructing peninsula) and the corresponding cross-sectional area left open are found and analysed. It is further analysed whether the depth-integrated model, usually adopted by others, is meaningful when applied to the water exchange problems. The flow through the channel narrowing is quantitatively estimated and compared with the three-dimensional results. The dynamics of the vortex structure and the identification of the up-welling/down-welling zones around the obstruction are discussed in detail. The influence of the transformation of the peninsula into a coastal island on the global basin circulation is considered as are the currents in the channel. The geometric and physical reasons for the anisotropy of the current structure which prevail through all obtained solutions are also discussed.Key words: Oceanography: general (limnology; numerical modeling) - Oceanography: physical (currents)

Barotropic wind-driven circulation patterns in a closed rectangular basin of variable depth influenced by a peninsula or an island

We study how a coastal obstruction (peninsula or coastal island) affects the three-dimensional barotropic currents in an oblong rectangular basin with variable bathymetry across the basin width. The transverse depth profile is asymmetric and the peninsula or island lies in the middle of the long side of the rectangle. A semi-spectral model for the Boussinesq-approximated shallow water equations, developed in Haidvogel et al. and altered for semi-implicit numerical integration in time in Wang and Hutter, is used to find the steady barotropic state circulation pattern to external winds. The structural (qualitative) rearrangements and quanti2tative features of the current pattern are studied under four principal wind directions and different lengths of the peninsula and its inclination relative to the shore. The essentially non-linear relationships of the water flux between the two sub-basins (formed by the obstructing peninsula) and the corresponding cross-sectional area left open are found and analysed. It is further analysed whether the depth-integrated model, usually adopted by others, is meaningful when applied to the water exchange problems. The flow through the channel narrowing is quantitatively estimated and compared with the three-dimensional results. The dynamics of the vortex structure and the identification of the up-welling/down-welling zones around the obstruction are discussed in detail. The influence of the transformation of the peninsula into a coastal island on the global basin circulation is considered as are the currents in the channel. The geometric and physical reasons for the anisotropy of the current structure which prevail through all obtained solutions are also discussed.Key words: Oceanography: general (limnology; numerical modeling) - Oceanography: physical (currents)

A Generalized Depth-Integrated Model of the Oceanic Mixed Layer

Abstract A generalized depth-integrated model of the oceanic mixed layer is developed by considering the heat and energy budgets of the upper ocean. Unlike the Kraus–Turner-type bulk models, the assumptions of an a priori well mixed layer and a positive density discontinuity at the base of the layer are not required in the present formulation. Relaxation of these restrictions is achieved by dealing directly with time-integrated equations, thus eliminating inaccuracies introduced by forming a differential equation prior to time discretization. The formulation involves a careful accounting of the effects of stratification below the mixed layer and the change in the density of the mixed layer produced by heat absorption and freshwater exchange. Scale analysis of the equation governing changes in mixed layer depth is used to reveal the conditions under which the present model reduces to a standard Kraus–Turner-type bulk model. Model results are compared with observations at OWS Papa in order to confirm the ut...

Simulation du bouchon vaseux dans l'estuaire de la Seine: capacité et limites d'un modèle bidimensionnel horizontal

Without any gravitational effect, a two-dimensional horizontal model simulates sediment patterns close to those observed in the Seine estuary. This result confirms the important role of the asymmetry of the tidal wave propagation and justifies the use of a depth-integrated model. But results show problems in long-term simulations of the turbidity maximum and excessive deposits along the coasts. A three-dimensional model seems to be necessary for mean-term simulations: the salinity gradients mainly act in maintaining the suspended particles in the estuary, while the vertical structure of velocities and concentrations help in avoiding the lateral sediment trapping.

A modelling study of tidally induced equilibrium sand balances in the North Sea during the Holocene

The present paper describes a depth-integrated modelling approach for tide-induced sediment transport, and its application to the North Sea for various cases during the Holocene sea level rise. The flow model is based on the shallow water equations, while the transport model is based on Galappatti’s asymptotic approach for rivers, now applied to tidal flow situations in two horizontal dimensions ( Galappatti, 1983, Galappatti and Vreugdenhil, 1986). The empirical Engelund–Hansen formula for sedimentation / erosion is used as a closure for the sediment exchange term in the transport equation, while variation of the bed height is neglected. The various assumptions in the derivation of the sediment model, and their consequences are addressed step by step. The North Sea area considered in the application is the whole North west European continental shelf, as mapped onto the Dutch Continental Shelf Model. In a series of cyclic period simulations of the present day situation, the sensitivity to parameter variations such as diffusion, equilibrium concentration and adaptation time is analysed, as well as the effect of bathymetry smoothing. Using a suitable and fixed parameter setting, the North Sea tidally induced equilibrium sand balances are simulated for several epochs during the Holocene sea level rise. Both uniform sea level reductions (0, −5, −15, and −35 m. and non-uniform sea level reductions (8500 BP, 8100 BP are considered, based on Jelgersma’s geological uniform sea level curve, and glacio-hydro-isostatic rebound modelling results, respectively. It is concluded that the derived Galappatti model for 2D tidal flow is a feasible approach to get a first assessment of equilibrium sedimentation balance on North Sea scale, and of its possible changes due to the Holocene sea level rise under various simplified assumptions regarding the evolution of coastline and bathymetry, both uniform and non-uniform.

Modelling tides and surface drift in the Arabian Gulf—application to the Gulf oil spill

A tide and surge forecasting model capable of predicting conditions for up to 5 days ahead has been developed to provide environmental data on tides, currents and particle trajectories in the Arabian Gulf. A two-dimensional depth-integrated model on a 5′ × 5′ grid of the entire Gulf, driven by a 10 constituent tidal forcing at the mouth near the Strait of Hormuz and by meteorological forecasts from the United Kingdom Meteorological Office global numerical weather prediction model was used to provide hourly distributions of the depth-averaged tidal and wind-driven currents. Following the discharge of oil from Mina Al Ahmadi into the Gulf in January 1991 an oil spill model was interfaced to the tide and surge model, providing forecasts of the movement and spread of the oil slick. The oil spill model used a three-dimensional particle tracking algorithm to model the dispersion of the oil so that surface and sub-surface concentrations could be determined. The effects of surface evaporation and decay of the oil were included in the model.

Theoretical analysis on depth-integrated modelling of suspended sediment transport

The depth-integrated model for suspended sediment transport based on the asymptotic solution of the convection-diffusion equation developed by Galappatti (Galappatti and Vreugdenhil, 1985) is gener...