Toward a general theory of the age in ocean modelling Eric J.M. Delhez a, * , Jean-Michel Campin b , Anthony C. Hirst c , Eric Deleersnijder b a GeoHydrodynamics and Environment Research, Universit e de Li  ege, Sart Tilman B5, B-4000 Li  ege, Belgium b Institut d'Astronomie et de G eophysique G. Lema ^ õtre, Universit e Catholique de Louvain, 2 Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium c CRC for Southern Hemisphere Meteorology, CSIRO Atmospheric Research, PMB 1, Aspendale Vic 3195, Australia Abstract Seawater is a mixture of several constituents. The age of a parcel of a constituent is de®ned 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 ¯ows 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 dierential 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. Ó 1999 Elsevier Science Ltd. All rights reserved. Keywords: Age; Age of seawater; Radioisotope; Tracer 1. Introduction Ocean ¯ows depend on a number of external forcings and phenomena which can be charac- terised by appropriate timescales, such as the inverse of the Coriolis parameter or the periods of tidal components. On the other hand, there are timescales which, instead of constraining the ¯ow, are inherent properties of the ¯ow which can be evaluated a posteriori, as diagnostic variables, to Ocean Modelling 1 (1999) 17±27 * Corresponding author. Tel.: +32-4-366-33-55; fax: +32-4-366-23-55. E-mail address: e.delhez@ulg.ac.be (E.J.M. Delhez) 1463-5003/99/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII:S1463-5003(99)00003-7