Conditions for the application of transport models to problems of environmental chemistry

It is pointed out that a physico-chemical approach to model the transport phenomena permits to describe dilution as a result of diffusive processes. In modelling real ecosystems this requires that the model reaches a steady state condition, in which the gradients of temperature and concentration, deriving from the continuos inputs and from the exchange through the open boundaries, are constant in time or vary slowly driven by seasonal driving forces. It can be proved that three dimensions are required for a model to have such features with constant diffusivities. Though the use of a constant diffusivity provides useful results, only time and space varying diffusivity tensors allow more detailed applications. It is here presented a methodology to derive such varying tensors basing on three-dimensional velocity fields, which can be used to this aim under a few conditions that are described. Finally, the ergodicity of the problem is discussed and it is proposed a method to estimate the shear stress both from velocity fields and from space and time varying diffusivity tensors.