Toward a general theory of the age in ocean modelling

Seawater is a mixture of several constituents. The age of a parcel of a constituent 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 an invaluable tool for understanding complex flows and the functioning of the numerical models used for representing them. A general theory of the age is developed, according to which the age of a constituent of seawater is a time-dependent, pointwise quantity that may be obtained from the solution of two partial differential equations governing the evolution of the concentration of the constituent under study and an auxiliary variable called the ``age concentration''. It is seen that previous applications of the notion of age are in agreement with the present theory, or may be viewed as approximations deriving from this theory. A few particular problems are touched upon, including the estimation of the age of the water and the determination of the age with the help of radioactive tracers