Oceanic age and transient tracers: Analytical and numerical solutions

Abstract

Transient tracers and the closely related “age” tracers exhibit a rich physical and mathematical structure even for problems of one space dimension. This richness tends to make interpretation of observations, which are inevitably thin in both space and time, difficult, in contrast to the situation in modeling studies. At least six different timescales and corresponding space scales can appear in one‐dimensional problems. In higher dimensions the number of scales increases. Several examples of analytical and numerical solutions are explored for the light they cast on understanding a fluid flow. Boundary Green functions emerge as the fundamental physical/mathematical link between interior tracer distributions and surface and other boundary variations. With transient tracers in inverse calculations one should normally use the underlying tracer distributions to attempt to solve for fundamental fluid properties, such as the mixing coefficients, rather than ambiguous “ventilation” times, which among other problems, may be determined only by the detection threshold and are often mainly functions of the tracer decay constant rather than of fluid properties. Tracers that are transient only through stochastic boundary conditions show that large‐scale space/time patterns can emerge in the tracer field, having little or no clear connection to the underlying fluid flow.