Eric Deleersnijder

The concept of age in marine modelling I. Theory and preliminary model results

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

Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region

Three turbulence closure schemes, designed for stratified shallow water flows, are presented. They are based upon k-epsilon theory and use respectively two, one or zero transport equations for turbulent variables. The models are first tested on the evolution of a wind-driven turbulent layer in a stratified fluid. The results are at least qualitatively in agreement with observational and experimental data. A discussion is given about the existence of self-similar solutions. The models are compared next with the observational data of the Rhine outflow area. The periodic variation in the density structure, forced by wind and tides and which is clearly visible in the data, is predicted by the model. A physical interpretation of the model results is given in the absence of wind forcing. The effects of estuarine circulation, tidal straining and mixing on the development or breakdown of stratification are well represented by the model calculations.

Sensitivity of a global coupled ocean‐sea ice model to the parameterization of vertical mixing

Three numerical experiments have been carried out with a global coupled ice-ocean model to investigate its sensitivity to the treatment of vertical mixing in the upper ocean. In the first experiment, a widely used fixed profile of vertical diffusivity and viscosity is imposed, with large values in the upper 50 m to crudely represent wind-driven mixing. In the second experiment, the eddy coefficients are functions of the Richardson number, and, in the third case, a relatively sophisticated parameterization, based on the turbulence closure scheme of Mellor and Yamada version 2.5, is introduced. We monitor the way the different mixing schemes affect the simulated ocean ventilation, water mass properties, and sea ice distributions. CFC uptake is also diagnosed in the model experiments. The simulation of the mixed layer depth is improved in the experiment which includes the sophisticated turbulence closure scheme. This results in a good representation of the upper ocean thermohaline structure and in heat exchange with the atmosphere within the range of current estimates. However, the en or in heat flux in the experiment with simple fixed vertical mixing coefficients can be as high as 50 W m(-2) in zonal mean during summer. Using CFC tracers allows us to demonstrate that the ventilation of the deep ocean is not significantly influenced by the paramertization of vertical mixing in the upper ocean. The only exception is the Southern Ocean. There, the ventilation is tao strong in all three experiments. However, modifications of the vertical diffusivity and, surprisingly, the vertical viscosity significantly affect the stability of the water column in this region through their influence on upper ocean salinity, resulting in a more realistic Southern Ocean circulation. The turbulence scheme also results in an improved simulation of Antarctic sea ice coverage . This is due to to a better simulation of the mixed layer depth and thus of heat exchanges between ice and ocean. The large-scale mean summer ice-ocean heat flux can vary by more than 15% between the three experiments. Because of this influence of vertical mixing on Southern Ocean ventilation, sea ice extent, and ocean-atmosphere heat fluxes, we recommend that global climate models adopt a sufficiently realistic representation of vertical mixing in the ocean.

Three-dimensional island wakes in the field, laboratory experiments and numerical models

Results of field, laboratory and numerical studies are used to describe the three-dimensional circulation in a barotropic island wake in shallow waters. Bottom friction generates a closed circulation characterized by a strong upwelling (typically 10-20 m h(-1)) in the bulk of the eddy and an even larger downwelling velocity in a narrow zone along the edges of the eddy. This downwelling exists at the solid boundaries of the island and also all along the separation streamline. This circulation can be realistically modeled numerically provided the intense turbulence in the free shear layers is explicitly parameterized. This secondary circulation aggregates buoyant material along the edges of the eddy even in well-mixed coastal waters. Copyright (C) 1996 Elsevier Science Ltd.

The water residence time in the Mururoa atoll lagoon: sensitivity analysis of a three-dimensional model

Abstract. The role of oceanic tide, wind stress, hoa inflow and stratification in the long-term circulation in Mururoa lagoon is investigated using a sensitivity analysis carried out by means of a three-dimensional model. Water renewal time scales are estimated. Wind stress is shown to be the dominant forcing. The hoa inflow slightly increases the turnover time, while stratification enhances the impact of motion in vertical planes parallel to the wind stress. The modelled turnover time is approximately 100 days, and becomes much larger than one year whenever the wind stress is disregarded.

Modelling the general circulation of shelf seas by 3Dk-ε models

Abstract One examines the modifications which must be made-and the limitations which must be set-to classical k-e models to extend their application to the simulation of marine mesoscale, synopticscale and macroscale processes which compose the weather-like and general circulations of the sea. The case of the general circulation—for which sub-grid scale fluctuations include such semi-organized motions as tides and storm surges-is discussed in more detail. A 3D k-e model appropriate to the study of the general circulation in a shallow stratified sea is presented and illustrated with the results of a simulation of the general summer circulation in the Northern Bering Sea, made in the scope of the NSF ISHTAR (“Inner Shelf Transfer and Recycling”) Program.

On the use of the sigma-coordinate system in regions of large bathymetric variations

The sigma-transformation is a widely used coordinate change that maps the actual depth-varying sea onto a computational domain, the depth of which is constant. The advantages of this technique are numerous. It permits an efficient use of computer resources, a simple treatment of the surface and bottom boundary conditions, and an accurate representation of the bathymetry. However, if the range of the depth is too large, or when the depth varies too rapidly, as in the shelf break region, it may be shown that the sigma-transformation leads to severe numerical errors. In the application of GHERs three-dimensional model to the Western Mediterranean, the occurrence of those numerical errors is avoided by the introduction of a two-fold sigma-coordinate system in the deep sea.

On the practical advantages of the quasi-equilibrium version of the Mellor and Yamada level 2.5 turbulence closure applied to marine modelling

The Mellor and Yamada level 2.5 turbulence closure model is briefly presented. It is argued that it might achieve an excellent compromise between accuracy and computer efficiency. It is, however, suggested that the stability functions are ill defined, leading to a marked lack of robustness, which manifests itself through the appearance of almost steady regions of exceedingly high shear. Theoretical reasoning shows that the seemingly less known quasi-equilibrium version of the level 2.5 model has more appropriate stability functions, rendering it more robust for marine modelling, where many different flow configurations are to be handled. This is strikingly illustrated by numerical experiments pertaining to the stress-driven penetration of a turbulent layer into a stratified fluid.

The concept of age in marine modelling II. Concentration distribution function in the English Channel and the North Sea

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

A 3-dimensional Model of the Water Circulation Around An Island in Shallow-water

A three-dimensional model is applied to the study of the tidal flow in the shallow waters around Rattray Island, Great Barrier Reef, Australia. The model uses the sigma-coordinate system and the numerical procedure is based on the finite volume approach. Two counter-rotating eddies develop in the wake of the island. The shearing and veering of the horizontal velocity is predicted to be small, hence the vertical motions are negligible almost everywhere, with the exception of some small regions. In the center of the eddies important upwelling is found, which is in qualitative agreement with theory and observations. The model exhibits strong downwelling along the upstream side of the island. Overall, the magnitude of the computed vertical motions may be too small and it is hypothesized that this may be due to a lack of resolution of the model. Further improvements to the model are outlined.