References of "Delhez, Eric"
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See detailCAT, The Constituent-oriented Age Theory, and its application to marine flows
Deleersnijder, Eric; Delhez, Eric ULiege; Mouchet, Anne ULiege et al

Conference (2002, May)

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See detailThe concept of age in marine modelling II. Concentration distribution function in the English Channel and the North Sea
Delhez, Eric ULiege; Deleersnijder, Eric

in Journal of Marine Systems (2002), 31(4), 279-297

The age of seawater and the age of real or idealized tracers are often used as diagnostic tools to better understand complex hydrodynamic flows. In most studies, the focus is on some averages of the ages ... [more ▼]

The age of seawater and the age of real or idealized tracers are often used as diagnostic tools to better understand complex hydrodynamic flows. In most studies, the focus is on some averages of the ages of the different particles making up a water parcel. The theory developed in Delhez et al. [Ocean Modell. I (1999) 17] and Deleersnijder et al. [J. Mar. Syst. 28 (2001) 229] provides, however, a more detailed description of the distribution of the ages of these particles through the so-called concentration distribution function. In this paper, the numerical aspects of the resolution of the evolution equation for the concentration distribution function in a five-dimensional space (time x 3D space x age dimension) are developed. Evolution equations for the moments of the concentration distribution function up to any order are also derived. A real case application of this theory to the simulation of the advection-dispersion of tracers (technetium-99) discharged at the nuclear fuel reprocessing plant of Cap de La Hague is described. The comparison of the results with those from previous studies demonstrates the advantages of the new method for the computation of the mean age. In particular, the method provides a detailed description of the temporal variations of the mean age only. The analysis of the full concentration distribution function and of its basic statistics shows that the standard deviation of the age of the different particles is far from negligible and should never be overlooked when analyzing age fields. A simplified analytical example suggests that the standard deviation of the age distribution is a measure of the integrated diffusion undergone by the tracer along its path from the source to the observation point. (C) 2002 Elsevier Science B.V All rights reserved. [less ▲]

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See detailTransient behaviour of water ages in the World Ocean
Deleersnijder, Eric; Mouchet, Anne ULiege; Delhez, Eric ULiege et al

in Mathematical & Computer Modelling (2002), 36(1-2), 121-127

The transient behaviour of the age of the water and that of the surface water is studied in the World Ocean. At any time and position, the age of the water, the age and the concentration of the surface ... [more ▼]

The transient behaviour of the age of the water and that of the surface water is studied in the World Ocean. At any time and position, the age of the water, the age and the concentration of the surface water are seen to obey a simple algebraic relation. The latter is illustrated by means of results of a three-dimensional World Ocean model and the analytical solution of an idealised, purely-diffusive, one-dimensional problem. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲]

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See detailResidual circulation and thermohaline distribution of the Ria de Vigo: a 3-D hydrodynamical model
Lopez, S. T.; Varela, R. A.; Delhez, Eric ULiege

in Scientia Marina (2001), 65(Suppl. 1), 277-289

A three-dimensional, non-linear, baroclinic model is described and tested for the first time to study the residual circulation and the thermohaline distribution of the Ria de Vigo (NW Spain) at short time ... [more ▼]

A three-dimensional, non-linear, baroclinic model is described and tested for the first time to study the residual circulation and the thermohaline distribution of the Ria de Vigo (NW Spain) at short time scales and under different wind stress regimes. Two markedly different realistic scenarios were chosen: northerly upwelling-favourable winds and southerly downwelling-favourable winds. The numerical experiments carried out indicate that the hydrodynamic regime of the Ria de Vigo is mostly a consequence of wind events. As could be expected, moderately strong North winds reinforce the normal (positive) Ria circulation, while winds blowing from the South, when sufficiently strong, reverse the typical circulation pattern and reduce the characteristic outgoing velocities and the flushing time inside the Ria. The temperature and salinity fields generated by the model in both situations were compared with observations and found to be in qualitatively good agreement, supporting the 3D velocity field distribution. [less ▲]

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See detailThe concept of age in marine modelling I. Theory and preliminary model results
Deleersnijder, Eric; Campin, Jean-Michel; Delhez, Eric ULiege

in Journal of Marine Systems (2001), 28(3-4), 229-267

The age of a particle of a seawater constituent is defined to be the time elapsed since the particle under consideration left the region, in which its age is prescribed to be zero. An Eulerian theory of ... [more ▼]

The age of a particle of a seawater constituent is defined to be the time elapsed since the particle under consideration left the region, in which its age is prescribed to be zero. An Eulerian theory of the age is presented, in which advection, diffusion, production and destruction phenomena are properly accounted for. The key hypothesis is that the mean age of a set of particles is to be evaluated as the mass-weighted average of the ages of the particles under study. The basic variable is the concentration distribution function, representing, at a given time and location, the distribution over the age of the concentration of the constituent being considered. This function satisfies a partial differential equation, which, upon appropriate integration over the age, yields the equations, in flux form, governing the evolution of the concentration and the age concentration. The ratio of the latter variable to the former is the mean age. Further theoretical developments are presented, including a thought experiment showing that mixing processes cause the ages of various constituents to be different from each other. The potential of the age as a tool for understanding complex marine flows is briefly demonstrated by analysing the results of two numerical models. The ages of a passive tracer, a radioactive tracer and the water are computed, along with a suitably defined radio-age. First, the fate of tracers released into the English Channel at La Hague is simulated. Then, ages are computed in the World Ocean as a measure of the time that has elapsed since leaving the surface layers. A theorem is demonstrated, which specifies that the age of the radioactive tracer must be smaller than the relevant radio-age, the latter being smaller than the age of the passive tracer, which, under appropriate hypotheses, can be seen to be equivalent to the age of the water. These inequalities seem to be remarkably robust, since they are found to hold valid in most of the numerical and analytical results examined in the present study. On the other hand, a dimensionless number is highlighted, which is believed to play an important role in the scaling of the differences between ages. (C) 2001 Elsevier Science B.V. All rights reserved. [less ▲]

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See detailIntegrated modelling of the Belgian Coastal Zone
Delhez, Eric ULiege; Carabin, G.

in Estuarine Coastal & Shelf Science (2001), 53(4), 477-491

The management of the water resources in coastal or delta plains asks for an integrated modelling of the water system at a regional scale. In the SALMON project, detailed descriptions of the groundwater ... [more ▼]

The management of the water resources in coastal or delta plains asks for an integrated modelling of the water system at a regional scale. In the SALMON project, detailed descriptions of the groundwater, river and marine domains are provided by coupling appropriate numerical models of these different sub-systems. The application of this three-fold model to the Scheldt and Belgian Coastal Zone reveals a marked river plume extending along the Belgian Coast with strong offshore gradients. This plume cannot be explained by the Eulerian residual transport velocity field but requires Lagrangian aspects to be taken into account. The computation of the age of this water mass shows that the different parts of the coastal zone are influenced by a discharge in the Grote Schijn River after a delay that varies between a few days (for the marine part of the estuary) to about 100 days (for the centre of the residual gyre). The computation shows also that the groundwater around Antwerp can also be contaminated by a pollution in the river but the resulting mass loss from the river does not lead to a significant reduction of the flux to the coastal zone. (C) 2001 Academic Press. [less ▲]

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See detailSome properties of generalized age-distribution equations in fluid dynamics
Beckers, Jean-Marie ULiege; Delhez, Eric ULiege; 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 ULiege; 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 ULiege; 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 ULiege 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 ULiege; Grégoire, Marilaure ULiege; Nihoul, Jacques ULiege 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 ULiege; Grégoire, Marilaure ULiege; Nihoul, Jacques ULiege et al

Poster (1998, May)

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See detailToward a general theory of the age in ocean modelling
Delhez, Eric ULiege; Campin, Jean-Michel; Hirst, Anthony et al

in Ocean Modelling (1998), 1

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See detailModelling Hydrodynamically Dominated Marine Ecosystems
Delhez, Eric ULiege

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

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

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 ULiege 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 ULiege; Nihoul, Jacques ULiege

Book published by Etienne Riga (1996)

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

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

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