RESUMO Este trabalho investiga a renovação das águas no Complexo Estuarino de Paranaguá (CEP), localizado no estado do Paraná, Brasil, usando o sistema de modelagem computacional SisBaHiA®. Um modelo de circulação hidrodinâmica, para a definição dos padrões de circulação, e um modelo de transporte Euleriano, para calcular a taxa de renovação (TR), idade da água (IA) e escoamento residual, foram implementados. A TR, a IA e o escoamento residual foram determinados para diferentes cenários hidrodinâmicos, com períodos representativos de verão e de inverno e, consequentemente, com diferentes forçantes (maré, vazão ou vento) com o objetivo de identificar as possíveis áreas de estagnação. Os resultados obtidos mostram que a maré e as vazões fluviais são os forçantes de maior importância na renovação das águas do CEP. Em todos os cenários foram identificadas duas possíveis áreas de estagnação, que apresentam menores TRs e maior IA, quando comparadas com outras regiões, a saber, a região da baía dos Pinheiros e a região próxima à cidade de Paranaguá. Durante o verão e considerando todos os forçantes, as TRs na região da baía dos Pinheiros e na região próxima à cidade de Paranaguá são menores que 95%, enquanto nas demais regiões do CEP os valores são superiores a 95%.

ABSTRACT This work investigates the water renewal in the Paranaguá Estuarine Complex (PEC), located in the state of Paraná, Brazil, using the SisBaHiA® computer modelling system. A hydrodynamic circulation model, for the definition of hydrodynamic circulation patterns, and an Eulerian transport model, for the computation of the water renewal rate, water age and residual circulation, were implemented. The water renewal rate, water age and residual circulation were computed for different hydrodynamic scenarios, with representative summer and winter periods and, consequently, with different forcings (tide, river flow or wind), in order to identify possible stagnation areas. Results show that the tide and the river flows are the most important forcings in the water renewal of the PEC. Two possible stagnation areas were identified in all scenarios, which presented lower renewal rates and higher water ages when compared to the other regions, namely, the Pinheiros bay region and the region near to Paranaguá city. During the summer and taking into account all the forcings, renewal rates in the Pinheiros Bay region and near the city of Paranaguá are less than 95% whereas in the other regions of the PEC, the values are higher than 95%.

This work presents a method for numerical simulation of viscous fluid flows based on the use of filtered Lagrangian Navier-Stokes equations. It is based on the hypothesis that the small scale motions are responsible for the homogenization of the physical properties in infinitesimal fluid parcels through a mixing process, mathematically expressed as a spatial filter, which implicitly works as an averaging operator. When the filter was applied to the Navier-Stokes equations for incompressible flows, in the Lagrangian frame of reference, the functional form of the resulting equations was preserved, and the number of unknowns remained the same as the number of available equations, therefore circumventing the need of an explicit subgrid scale model. The method was validated by performing two-dimensional simulations of high Reynolds number wake flows. It was verified that the main large scale characteristics of the flows were properly replicated.