Water renewal of a region of freshwater influence (ROFI): mathematical properties of some of the relevant diagnostic variables
(2019) , 19 pages
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- Abstract
- We first lay out the partial differential problems governing the concentrations of the water types (the original, river and coastal ocean waters) and their aggregates (the renewing water and the water itself) that help gain insight into the water renewal processes of a generic region of freshwater of influence (ROFI). We establish the mathematical properties of these concentrations, showing that they are well behaved. Then, in the framework of the Constituent-oriented Age and Residence time Theory (CART, www.climate.be/cart), we show how to evaluate the age (time elapsed since leaving the relevant open boundary) of the above water types and their aggregates, which are treated as passive tracers. We demonstrate that the ages satisfy criteria suggesting that the diagnostic strategy outlined herein is well founded. Finally, we set up a highly-idealised, steady-state, one-dimensional illustration, allowing us to obtain closed-form solutions. The age of the river and coastal ocean waters are seen to be symmetric with respect to the centre of the domain of interest. This unexpected property has yet to be explained. We believe that some of the present mathematical developments are part of the activities that should be carried out in order to validate a diagnostic strategy based on time- and position-dependent timescales.
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Citations
Deleersnijder, E. (2019). Water renewal of a region of freshwater influence (ROFI): mathematical properties of some of the relevant diagnostic variables. https://hdl.handle.net/2078.5/94539