The concept of age in marine modelling: 1. Theory and preliminary model results
Deleersnijder, E.; Campin, J.M.; Delhez, E.J.M. (2001). The concept of age in marine modelling: 1. Theory and preliminary model results. J. Mar. Syst. 28(34): 229267. dx.doi.org/10.1016/S09247963(01)000264
In: Journal of Marine Systems. Elsevier: Tokyo; Oxford; New York; Amsterdam. ISSN 09247963; eISSN 18791573, more
 
Keywords 

Author keywords 
age; age of seawater; radioisotope; tracer; World Ocean; English channel; North Sea 
Authors   Top 
 Deleersnijder, E., more
 Campin, J.M.
 Delhez, E.J.M., more



Abstract 
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 massweighted 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 radioage. 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 radioage, 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. 
