References of "Beckers, Jean-Marie"
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See detailMetal fluxes through the Strait of Gibraltar: the influence of the Tinto and Odiel rivers (SW Spain)
Elbaz-Poulichet, F.; Morley, N. H.; Beckers, Jean-Marie ULg et al

in Marine Chemistry (2001), 73(3-4), 193-213

A large set of new data concerning dissolved metal concentrations has been acquired in the Gulf of Cadiz and in the Strait of Gibraltar from 1996 to 1999. These data, associated with models (hydrodynamic ... [more ▼]

A large set of new data concerning dissolved metal concentrations has been acquired in the Gulf of Cadiz and in the Strait of Gibraltar from 1996 to 1999. These data, associated with models (hydrodynamic, tracer advection-dispersion and mixing), have been used to assess the influence of rivers draining the South Iberian Pyrite Belt on the Gulf of Cadiz and on the Atlantic inflow in the Strait of Gibraltar. Metal concentrations in surface waters from the Gulf of Cadiz are maximal near the mouth of the Tinto/Odiel rivers with values exceeding 50 nmol/kg (Mn), 5 nmol/kg (Ni), 30 nmol/kg (Cu), 100 nmol/kg (Zn), 0.9 nmol/kg (Cd) and 45 nmol/kg (As). From the Tinto/Odiel river, a plume of contamination follows the coast in the direction of the Strait of Gibraltar. The computation of a tracer advection-dispersion model confirms that the coastal currents carry the metals discharged from the Tinto and Odiel to the Strait of Gibraltar. From temperature-salinity and metal-salinity plots, four water masses can be recognised in the Gulf of Cadiz and in the Strait of Gibraltar: North Atlantic Surface Water (NASW), North Atlantic Central Water (NACW) and metal-enriched Spanish Shelf Waters from the Gulf of Cadiz (SSW). The Mediterranean Outflow Water (MOW) is also clearly seen at depths greater than 300 m. The chemical characteristics of these various water masses have been used in a mixing model to evaluate their relative contribution to the Atlantic inflow through the Strait of Gibraltar. These contributions are seasonally variable. in June 1997, the contribution was: 80 +/- 20%, 5 +/- 5% and 15 +/- 10% for NASW, NACW and SSW, respectively. In September, the SSW contribution was apparently negligible. Finally, these relative contributions allow the evaluation of the metal fluxes in the Strait of Gibraltar. The presence of SSW in the Strait increases the metal flux to the Mediterranean Sea by a factor of 2.3 (Cu), 2.4 (Cd), 3 (Zn) and 7 (Mn). It does not modify significantly As and Ni fluxes. (C) 2001 Published by Elsevier Science B.V. [less ▲]

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See detailSome properties of generalized age-distribution equations in fluid dynamics
Beckers, Jean-Marie ULg; Delhez, Eric ULg; Deleersnijder, Eric

in SIAM Journal on Applied Mathematics (2001), 61(5), 1526-1544

The concept of age in fluid dynamics is analyzed in the case of a tracer advection-diffusion equation. From the general solution in a uniform velocity field, it is shown that unexpected symmetry ... [more ▼]

The concept of age in fluid dynamics is analyzed in the case of a tracer advection-diffusion equation. From the general solution in a uniform velocity field, it is shown that unexpected symmetry properties arise for the age field. In particular, for a point release, the age field is isotropic, regardless of the direction of the ow and the value of the diffusion coefficient. The analysis is then extended to situations with time-varying currents, where the symmetry can be broken under some circumstances. Finally, we show a method by which a time-dependent problem can be used to assess a stationary concentration distribution function, providing details about the propagation of younger and older material at a given location. [less ▲]

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See detailOn the symmetry of the age field of a passive tracer released into a one-dimensional fluid flow by a point-source
Deleersnijder, E.; Delhez, Eric ULg; Crucifix, M. et al

in Bulletin de la Société Royale de Liège (2001), 70

Tracer is released from a point-source into an incompressible, one-dimensional fluid flow, with constant velocity and diffusivity. The age of a tracer parcel, which is defined as the time elapsed since ... [more ▼]

Tracer is released from a point-source into an incompressible, one-dimensional fluid flow, with constant velocity and diffusivity. The age of a tracer parcel, which is defined as the time elapsed since leaving the source, may be evaluated as the ratio of the age concentration to the tracer concentration. The latter are governed by two partial differential equations. Time-dependent analytical solutions are derived, which show that the age is symmetric with respect to the source. This is astonishing, since it could have been expected that the age would reflect somehow the strong asymmetry of the tracer concentration, which tends to be much larger on the downstream side of the source than on the upstream side. Some finite-difference counterparts of this problem are seen to lead to age fields which, in their steady-state limit, are also symmetric with respect to the source. This is believed to be helpful to interpret the results of numerical models of complex fluid flows in which the age is introduced as a diagnostic variable. [less ▲]

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See detailThe age, a tool for understanding complex fluid flows
Deleersnijder, E.; Beckers, Jean-Marie ULg; Campin, J.-M. et al

Conference (2000, May)

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See detailSensitivity of the black sea's ecosystem to physical processes: first results of a high resolution 3D interdisciplinary model
Grégoire, Marilaure ULg; Beckers, Jean-Marie ULg; Nihoul, Jacques ULg et al

in Balopoulos, E.; Chronis, G.; Lipiatou, E. (Eds.) et al International conference. Oceanography of the eastern Mediterranean and Black Sea. Similarities and differences of two interconnected basins (2000)

A hydrodynamical model of the general circulation in the Black Sea has been build up, using the GHER (GeoHydrodynamics and Environment Research) three-dimensional, non-linear, baroclinic, turbulent ... [more ▼]

A hydrodynamical model of the general circulation in the Black Sea has been build up, using the GHER (GeoHydrodynamics and Environment Research) three-dimensional, non-linear, baroclinic, turbulent closure model. A model with 5 km horizontal resolution and 25 vertical levels is used to compute the typical seasonal cycle by forcing the model with climatological monthly mean fields of temperature, salinity and wind stress at the air-sea interface. Furthermore, the river discharges of the Danube, the Dnestr and the Dnepr are taken into account. This high resolulion model resolves the baroclinic instabilities generated by the interactions of the boundary current with the coastline geometry or with the continental shelf/slope topography. A simple ecosystem model defined by a nitrogen cycle is coupled with Ihe hydrodynamical model. The state variables of this model are defined as those which are necessary and sufficient to assess the effects of the physical processes, and in particular of the boundary current instability , on the space time distribution of the primary and secondary productions. The results of the 3D ecohydrodynamic model are compared with CZCS data of surface chlorophyll fields collected during the period from 1978 to 1986. [less ▲]

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See detailModeling the Black Sea and the Mediterranean Sea hydrodynamics: a comparative study
Beckers, Jean-Marie ULg; Elmoussaoui, A.; Rixen, M. et al

in Balopoulos, E.; Chronis, G.; Lipiatou, E. (Eds.) et al International conference. Oceanography of the eastern Mediterranean and Black Sea. Similarities and differences of two interconnected basins, Zappeion international conference Centre (2000)

The application of the GHER 3D primitive equation model to the simulation of the seasonal cycle of the Mediterranean and Black Sea circulation will be shown. The two basins are very illustrative for ... [more ▼]

The application of the GHER 3D primitive equation model to the simulation of the seasonal cycle of the Mediterranean and Black Sea circulation will be shown. The two basins are very illustrative for either concentration or dilution basins, and modelling such different systems needs some special attention with respect to the representation of the water masses and mixing between the different layers. The strength of the variability of both basins will be compared, including comparison with climatological data. Turbulent characteristics in both cases alalysed, showing that at the scales under investigations, both turbulent regimes are close to a balance between production, destruction and vertical diffusion of turbulence. ft is also shown how the river dominaled Black Sea exhibits specific free surface behaviors while the Mediterranean Sea exhibits specific deep water formations leading both to a different kind of vertical mixing. [less ▲]

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See detailCirculation and coastal processes off NW Africa
Elmoussaoui, Abdellali; Djenidi, Salim ULg; Kostianoy, Andrey et al

in Oceanic Fronts and Related Phenomena : Konstantin Fedorov International Memorial Symposium Proceedings (2000)

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See detailNumerical discretization of rotated diffusion operators in ocean models
Beckers, Jean-Marie ULg; Burchard, Hans; Deleersnijder, Eric et al

in Monthly Weather Review (2000), 128(8), 2711-2733

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on ... [more ▼]

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on the so-called z-coordinate system is presented. The authors then focus exclusively on the dynamically passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather complex, while simpler, linear schemes are shown to produce unphysical undershooting and overshooting. It is suggested that the choice of an appropriate discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically active or not. [less ▲]

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See detailA numerically efficient data analysis method with error map generation
Rixen, M.; Beckers, Jean-Marie ULg; Brankart, J. M. et al

in Ocean Modelling (2000), 2

The variational inverse model (VIM) for data analysis was already shown to be statistically equivalent to objective analysis (OA) provided the covariance function for the OA and the VIM reproducing kernel ... [more ▼]

The variational inverse model (VIM) for data analysis was already shown to be statistically equivalent to objective analysis (OA) provided the covariance function for the OA and the VIM reproducing kernel are identical. The VIM, however does not allow a direct derivation of the error field associated with the analysis. The purpose of the paper is to extend the one to one correspondance between the two analysis shemes by proposing a heuristic statistical error expression for the VIM. The numerical efficiency on analysis and error map generation of both methods is compared on quasi-synoptic and climatological data sets. It is shown that the VIM analysis and error map generation offers interesting numerical skills in both case studies. [less ▲]

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See detailSome theoretical and modelling aspects of the age as a tool for understanding marine flows
Deleersnijder, E.; Campin, J. M.; Beckers, Jean-Marie ULg et al

in Alonso Del Rosario, J. L.; Gallego, F. O. (Eds.) Actas de la II Jornadas de análisis de variables y simulación numérica del intercambio de masas de agua a través del estrecho de Gibraltar (2000)

The age of a parcel of a constituent of seawater is defined to be the time elapsed since the parcel under consideration left the region where its age is prescribed to be zero. Estimating the age is thus ... [more ▼]

The age of a parcel of a constituent of seawater is defined to be the time elapsed since the parcel under consideration left the region where its age is prescribed to be zero. Estimating the age is thus an invaluable tool for understanding complex oceanic flows and the functioning of the numerical models used for representing them. In this paper, a general theory of the age is presented, in which advection, diffusion, production and destruction are properly accounted for. The partial differential equations used for the rigorous computation of the age as a function of space and time are established. This general theory is applied to the computation of the ventilation rates in the World Ocean. The results are compared with those of widely used carbon-14-like dating techniques. Using both numerical simulations and analytical developments, it is shown that the age of the radioactive tracer is smaller than the carbon-14-like age, which is larger than that of the passive tracer. The latter is equivalent to the ventilation or water age. The difference between the various ages, which is essentially due to the influence of mixing processes, increases as the timescale of decay of the radioactive tracer decreases [less ▲]

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See detailOn some stability properties of the discretization of damped propagation of shallow-water inertia–gravity waves on the Arakawa B-grid
Beckers, Jean-Marie ULg

in Ocean Modelling (1999), 1(2-4), 53-69

We investigate a problem mentioned by Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2), who looked at the problem of the discretization of inertia–gravity waves ... [more ▼]

We investigate a problem mentioned by Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2), who looked at the problem of the discretization of inertia–gravity waves in the staggered B-grid. We generalize this study by adding diffusion. General stability conditions are found with the help of Miller's theorem, and the paradox found in Deleersnijder and Campin (Deleersnijder, E., & Campin, J. -M. (1993). Ocean Modelling 97, 2) is discussed. It is argued that it stems from inappropriate application of boundary conditions in conjunction with a Coriolis force treatment which could produce mechanical work. [less ▲]

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See detailDissection of the GHER turbulence closure scheme
Delhez, Eric ULg; Grégoire, Marilaure ULg; Nihoul, Jacques ULg et al

in Journal of Marine Systems (1999), 21(1-4), 379-397

In this paper, the turbulence closure scheme implemented in the GHER hydrodynamic model is described in detail. Two case studies carried out in two contrasting conditions-one in the shallow, tide ... [more ▼]

In this paper, the turbulence closure scheme implemented in the GHER hydrodynamic model is described in detail. Two case studies carried out in two contrasting conditions-one in the shallow, tide dominated, north-western European continental shelf, and the other in the deep Mediterranean Sea-are used to identify the dominant terms of the equation for the turbulent kinetic energy, first theoretically, secondly from the results of the simulations. In both domains, the dominant terms are the local destruction and production terms, the vertical diffusion term and to a smaller degree, the time derivative. Advection and horizontal diffusion turn out to be negligible in most of the relevant cases for such large scale studies. This opens the way to simplifications and optimisations of the numerical models. (C) 1999 Elsevier Science B.V. All rights reserved. [less ▲]

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See detailAccuracy and stability of the discretised isopycnal mixing equation
Mathieu, P. P.; Deleersnijder, E.; Beckers, Jean-Marie ULg

in Applied Mathematics Letters (1999), 12(4), 81-88

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See detailBarotropic and baroclinic oscillations in strongly stratified ocean basins - Numerical study of the Black Sea
Stanev, Emil; Beckers, Jean-Marie ULg

in Journal of Marine Systems (1999), 19(1-3), 65-112

We investigate barotropic and baroclinic oscillations in strongly stratified basins using the Black Sea as a test case. The GHER 3D-model, which has active free surface and temperature and salinity fields ... [more ▼]

We investigate barotropic and baroclinic oscillations in strongly stratified basins using the Black Sea as a test case. The GHER 3D-model, which has active free surface and temperature and salinity fields as scalar state variables produces model results which are then analysed with a focus on barotropic and baroclinic waves at different scales. The model is forced by seasonally variable climatic data and river run-off. High frequency oscillations of the sea level simulated by the model are compared against observations. It is found that phases and amplitudes are simulated realistically. For the density field, long internal gravity waves dominate the solution in the sub-inertial range, The amplitudes of these oscillations increase over the continental slope, which provides an efficient mechanism for mixing in the western Black Sea. It is found that the sea surface oscillations interact with the oscillations in the pycnocline. This interaction could contribute to a modification of the vertical stratification in a long run. The vertical stratification, on its side, jointly with the bottom relief causes different appearances of oscillations over the continental slope and in the basin interior. Changes in the stability of stratification, caused by the seasonal cycle, are thus an important factor modifying wave processes and the resulting internal mixing. (C) 1999 Elsevier Science B.V. All rights reserved. [less ▲]

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See detailApplication of Miller's theorem to the stability analysis of numerical schemes; some useful tools for rapid inspection of discretisations in ocean modelling
Beckers, Jean-Marie ULg

in Ocean Modelling (1999), 1

An old theorem about the roots of a polynomial is resurfaced and examined, focusing on the practical question of determining stability criteria for numerical schemes. Is is demonstrated that the theorem ... [more ▼]

An old theorem about the roots of a polynomial is resurfaced and examined, focusing on the practical question of determining stability criteria for numerical schemes. Is is demonstrated that the theorem can be useful both for analytical studies of the stability limits, as well as numerical searches for stability regions. It is particularly important that when deciding whether the scheme is stable or not, it is not necessary to search for the roots of the polynomial. Indeed, such a decision may be reached through a finite and small number of arithmetic operations and verifications of inequalities. In addition to the analysis of the theorem, some practical conditions for polynomial of different orders are presented, as well as some useful tips on how simply necessary or sufficient stability conditions can be obtained. [less ▲]

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See detailCoupled 3D eddy-resolving general circulation model and ecosystem model applied to the Black sea.
Grégoire, Marilaure ULg; Beckers, Jean-Marie ULg; Nihoul, Jacques ULg et al

in Ostrovskii, S.; Zatsepin, A. (Eds.) Oceanic Fronts and Related Phenomena (Konstantin Federov International Memorial Symposium) (1999)

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See detailNumerical simulations of seasonal and interannual variability of the Black Sea thermohaline circulation
Stanev, Emil; Beckers, Jean-Marie ULg

in Journal of Marine Systems (1999), 22(4), 241-267

The Black Sea general circulation is simulated by a primitive equation model with active free surface. The forcing is seasonally variable and is based on available climatic data. The model reproduces the ... [more ▼]

The Black Sea general circulation is simulated by a primitive equation model with active free surface. The forcing is seasonally variable and is based on available climatic data. The model reproduces the main features of the Black Sea circulation, including the river discharge effects on the mean sea level and the Bosphorus outflow. Model results show that the simulated sea surface elevation increases in spring over the whole sea, reaching a maximum in the Danube delta area. In the same region, a minimum is observed in winter. The amplitude of the seasonal oscillations (about 8-12 cm over the whole basin) is of the same order of magnitude as the maximum horizontal variations (about 15-18 cm between the coastal areas and the basin interior). This strong signal formed mostly by river discharges, along with the seasonal variability in the other forcing functions and the local dynamics creates a well-pronounced interannual variability. The performance of the model in simulating the seasonal and interannual variability is critically analyzed, with a special attention on the cold intermediate water formation and the circulation in the upper 150 m. The simulations demonstrate that the source of intermediate waters is on the shelf, and that the water mass in the core of cold intermediate layer changes with time as a response to the periodic forcing at sea surface. This type of variability is characterized by pronounced interannual changes, proving that important differences could exist between water mass structure in different years, even when using identical atmospheric forcings each year. (C) 1999 Elsevier Science B.V. All rights reserved. [less ▲]

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See detailDissection of the GHER Turbulence Closure Scheme
Delhez, Eric ULg; Grégoire, Marilaure ULg; Nihoul, Jacques ULg et al

Poster (1998, May)

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