This paper deals with transport processes and circulation patterns in a coastal area where bays interact with an upwelling centre. We focus on the coastal water along the meridional coastline of the Rio de Janeiro state, where the spatial variability of hydrodynamics characteristics is considerably greater than in open sea. Particular emphasis is given on the physical processes related to countercurrent flows. To study those processes an extended gravity reduced model for open marine regions is used taking into account the hydrodynamic and thermodynamic of coastal zone waters. To solve the non-permanent hydro-thermodynamic governing equations, a Petrov-Galerkin (PG) finite element model for open-area domain is proposed. Using a set of idealised wind field patterns, some numerical experiments are performed showing typical hydrodynamical features of that coastal area, such as: upwelling plumes, warming influences of the bays in the surrounding sectors and the coastal countercurrent flows.