The concept of age in marine modelling: 2. 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. 1 (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