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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 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 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 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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See detailModelling Hydrodynamically Dominated Marine Ecosystems
Delhez, Eric ULg

in Journal of Marine Systems (1998), 1-2

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See detailMacroscale ecohydrodynamic modeling on the Northwest European Continental Shelf
Delhez, Eric ULg

in Journal of Marine Systems (1998), 16(1-2), 171-190

A 3D coupled hydrodynamic-biological model is applied to the simulation of the biological processes on the Northwest European Continental Shelf. The model operates in the macroscale spectral window (time ... [more ▼]

A 3D coupled hydrodynamic-biological model is applied to the simulation of the biological processes on the Northwest European Continental Shelf. The model operates in the macroscale spectral window (time scales of a month or a season) without explicit description of the higher frequency processes but with an adequate modeling of their influence on larger time scales. The hydrodynamic sub-model is 3D, baroclinic and includes a refined turbulence closure. The non-linear interactions of mesoscale fluctuations are described by means of the generalized mesoscale Reynolds stresses and the Stokes drift transport velocity field. The biological sub-model describes the nitrogen and carbon cycles through the food web with 17 state variables representing 9 compartments: inorganic nutrients, small phytoplankton, large phytoplankton, dissolved organic matter, pelagic bacteria, heterotrophic flagellates, pelagic detritus, zooplankton and benthic organic detritus. The simulation emphasizes the strong influence of the local depth and of the stability of the water column on the whole annual cycle of phytoplankton. In well-mixed shallow areas, the chlorophyll concentration increases in early spring and the primary production occurs steadily until October. In deeper areas, the spring bloom is much sharper and appears later, after the set up of the seasonal stratification. The main part of the primary production happens during the bloom period. The macroscale approach provides results that are comparable with observations and results of other more classical models describing explicitly the higher frequency processes. The current method allows, however, a more direct insight into the dynamics of the system and into the interactions between the hydrodynamics and the biology. Also, it greatly reduces the CPU requirements and is therefore particularly suited for repeated or long term simulations. (C) 1998 Elsevier Science B.V. All rights reserved. [less ▲]

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See detailSea air land modelling operational network
Ghiot, C. B.; Bauler, P.; Beckers, Jean-Marie ULg et al

in Lecture Notes in Computer Science (1997), 1225

The purpose of the SALMON project is to develop a single model from three previously existing models (ocean, river and groundwater) for the description of environment quality in a whole system of regional ... [more ▼]

The purpose of the SALMON project is to develop a single model from three previously existing models (ocean, river and groundwater) for the description of environment quality in a whole system of regional scale including marine, river, groundwater and atmospheric inputs. The connection of the different models is done through a specific interface, a junction, designed to allow the data exchange between models based on different numerical methods. The software is developed on IBM RS/6000 computers (the SP2 parallel machine). [less ▲]

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See detailMécanique Rationnelle - Modèle Mathématique de Newton
Delhez, Eric ULg; Nihoul, Jacques ULg

Book published by Etienne Riga (1996)

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See detailModelling the North Sea hydrodynamics in a management perspective
Djenidi, Salim ULg; Delhez, Eric ULg; Martin, Géraldine ULg et al

in Bulletin de la Société Royale des Sciences de Liège (1996), 65

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See detailReconnaissance of the general circulation of the North-Western European Continental Shelf by means of a three-dimensional turbulent closure model
Delhez, Eric ULg

in Earth-Science Reviews (1996), 41(1-2), 3-29

The general circulation of the North-Western European Continental Shelf is investigated by means of a three-dimensional macroscale mathematical model. Results corresponding to typical winter and summer ... [more ▼]

The general circulation of the North-Western European Continental Shelf is investigated by means of a three-dimensional macroscale mathematical model. Results corresponding to typical winter and summer conditions are described in detail. Prominent features are explained from a dynamic point of view by referring to the main forcing factors of the macroscale circulation on the North-Western European Continental Shelf: seasonal mean wind stress and atmospheric pressure, large a scale sea surface slope, non-linear interactions of the higher frequency processes and density differences. The role of the bottom topography is also highlighted. The largest seasonal variations are mainly due to the occurrence of a thermal stratification in summer over large parts of the shelf. In such conditions, there is only a weak interaction between the surface and bottom layers that have therefore significantly different dynamics. [less ▲]

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See detailOn the residual advection of passive constituents
Delhez, Eric ULg

in Journal of Marine Systems (1996), 8(3-4), 147-169

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 ... [more ▼]

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. (1986a) 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. [less ▲]

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See detail3D turbulence field on the north-western european continental-shelf
Martin, Géraldine ULg; Delhez, Eric ULg

in Tellus : Series A (1994), 46(2), 98-112

The 3-dimensional, non-linear, baroclinic, GHER mathematical model for the study of mesoscale motions (time scale of several hours to several days: tides, storm surges, ...) is described. Particular ... [more ▼]

The 3-dimensional, non-linear, baroclinic, GHER mathematical model for the study of mesoscale motions (time scale of several hours to several days: tides, storm surges, ...) is described. Particular attention is paid to the turbulent closure based on an evolution equation for the turbulent kinetic energy and a parametric expression of the mixing length (k-model). Appropriate boundary conditions and numerical techniques (mode-splitting, implicity, sigma-coordinate system, advection scheme) are described. The model is applied to the simulation of the M2 tide on the North-Western European Continental Shelf not only without wind but also in typical winter and summer conditions. Large spatial variations of the turbulent kinetic energy appear as a result of the variations of depth and tidal activity around the shelf. These variations are clearly related to the different turbulence regimes observed in summer, with frontal structures separating well-mixed waters from stratified ones. The structure and evolution of the vertical profiles of turbulence variables are described and explained in barotropic and baroclinic conditions, under different wind forcings. The evolution of these profiles at the M2 tide frequency largely depends on the eccentricity of the tidal ellipse. [less ▲]

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See detailPRELIMINARY-RESULTS OF 3-D BAROCLINIC NUMERICAL-MODELS OF THE MESOSCALE AND MACROSCALE CIRCULATIONS ON THE NORTH-WESTERN EUROPEAN CONTINENTAL-SHELF
Delhez, Eric ULg; Martin, Géraldine ULg

in Journal of Marine Systems (1992), 3(4-5), 423-440

Two mathematical models for the study of mesoscale (tides, storm surges ...) and macroscale (general circulation ...) motions are described. Both models are derived from the GHER 3-D baroclinic turbulent ... [more ▼]

Two mathematical models for the study of mesoscale (tides, storm surges ...) and macroscale (general circulation ...) motions are described. Both models are derived from the GHER 3-D baroclinic turbulent closure primitive equation model and adapted to the specific spectral windows of, respectively, mesoscale and macroscale processes. Numerical methods are discussed: 3-D finite differences, mode-splitting, sigma-transform ... The mesoscale model is applied to the simulation of the M2 tide on the North-Western European Continental Shelf. The residual circulation model is based on time averaged primitive equations which explicitly include mesoscale Reynolds stresses that are computed by the mesoscale model. Preliminary results of the application of this model in typical summer conditions are presented. [less ▲]

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