Throwing 2 pieces of wood in to the water   

Many researchers are interested in these worrying different phenomena. The oceanographic boat ‘Belgica’ regularly surveys our coastal waters and the Escaut river estuary to allow biologists and chemists to take water samples and analyse them. Another line of research is that of the mathematical and numeric modeling of pollution. This is the path chosen by Professor Eric Delhez (General Mathematics, Faculty of Applied Sciences), who has just published an article in the Journal of Marine Systems about the transport of pollutants in the Scheldt estuary. “Our model is aimed at predicting the transport of pollutants in the estuary. The overall objective is to develop tools which highlight political choices or town and country planning, from limiting the sources of pollution to even predicting the consequences of an industrial accident.”

To illustrate the difficulty of such a model with an image, all you have to do is throw two pieces of wood in to the source of the Escaut in Gouy in the north of France, and wait at the mouth in Antwerp 360km further down to see if they arrive side by side at the same time.  Obviously not! There are so many factors which can influence their journey. A river, states Eric Delhez, is not a simple pipeline. It is an open system: the river runs in to the sea but the tides retroact on the system. (In the Escaut, the tide is felt up to 150km from the mouth.) A section of a pipeline is homogenous, but that of a river varies from one place to another: in the Escaut estuary, you can find sand banks, riverbanks, oak trees… the nature of the soil also varies: sand, mud, gravel. The difficulty with such a model is also the time scale. Our two pieces of wood will take several weeks to travel down the Escaut. During this time lapse, the weather can fluctuate and the wind and the rain are obviously going to influence the flow, from one day to another, from week to week, from one season to another, from one year to the next. The system is very complex but today, computers are powerful enough to integrate all these variables.

More difficult to model a cube than a square   

The first hydrodynamic models appeared thirty years ago. One of the pioneers in this field was Professor Jaques Nihoul of the University of Liege, who created the first North Sea mathematical model. It was at the time of two dimensional models, designed to predict the height of the tides and protect the coasts from the effects of storms. Once the calculators became powerful enough, in the 1990’s, the first three- dimensional models appeared that took in to account the water column. “We are no longer confronted with a square, resumes Eric Delhez, but with a cube! It’s 100 times more complicated.” Certainly the basic laws are those of Newton, like for example F = ma (Force = mass x acceleration). A law which, by the way, is just as relevant for a fluid as for a car or a runner. But to grasp the hydrodynamics of an estuary, we must invent other equations, which take in to account the variables observed in the field.

(1) DELHEZ E. & WOLK F., Diagnosis of the transport of adsorbed material in the Scheldt estuary: A proof of concept, Journal of Marine Systems, 0924-7963 (in press)