Mathematical models applied to tracer studies of coastal water dynamics in Montevideo city, Uruguay

Abstract

With the purpose of furnishing a suitable reference framework to develop the mathematical models that are the main objective of this research, the first part of the article summarizes the fieldwork carried out in the coastal waters of the Río de la Plata in the Montevideo region and in the Bay of Montevideo between 1991 and 2001. We begin with the results of a study of the dynamics and renewal of water in the bay of Montevideo that involved the use of radioactive and fluorescent tracers injected in the water inside the bay. During this study, the detection of artificial radioactivity due to tritium, 15 km east from the bay’s mouth, led to the conclusion that there is a process of breakers diffusion in the strip of adjacent coastal waters located to the east of said mouth. In order to distinguish between the contributions of the Punta Brava sub-aquatic sewage outfall and the contributions of the contamination of the bay, studies of the influence of the bay on the coastal waters were carried out simultaneously with a study of the dynamics of the sewage outfall discharge plume. During these works a significant trap effect was discovered at Pocitos beach. This effect was investigated using fluorescent tracers to simulate a localized contamination event. A study of sediment dynamics was carried out in the Bay of Montevideo and adjacent coastal waters using radioactive tracers. In addition, information related to dredging processes was obtained using density probes. The self-purification capacity of the coastal waters in the Punta Lobos region (where it is planned to locate the second sub-aquatic emitter of the city of Montevideo) was determined using a double tracer method. In the second part of the article we review and discuss the mathematical models (analytical models) constructed and used to design and interpret the results of the field work summarized in the first part. We start with the compartment models constructed for a parametric characterization of the water renewal kinetics in the Bay of Montevideo, including a classical two compartments model and s recent model three compartments model based on fractal kinetics. We summarize the mathematical models used field work in coastal waters, either for forecasting purposes (for radiological protection and design of experiments) or for diagnostic purposes (for parametric characterization of transport processes from experimental results). The mathematical model constructed for the determination of T90 in the coastal waters adjacent to Punta Lobos is reviewed.