In this paper a numerical model, which describes the current system and transport processes of coastal ocean regions under wind field forcing, is presented. The model has an active layer overlaying a deep inert layer where the pressure gradient is set to zero. The model includes the turbulent version of the momentum and continuity equations and transport equations to describe the thermodynamic changes of the sea surface temperature (SST) and the changes of pollutants. Solutions are found numerically on a uniform grid and the fundamental equations are approximated by the finite difference method taking the form of a Lax-Wendroff scheme. Solutions forced by uniform and non-uniform wind fields are evaluated for a schematic straight coastline and for the coastal area of Cabo Frio (Rio de Janeiro, Brazil). The solutions for the coastal area of Cabo Frio differ considerably depending on the orientation of the winds. All the solutions show a very sensitive response of the currents and SST. Solutions forced by an idealized representation of a non-uniform wind field develop a SST pattern similar as the observations, particularly the extension of the cool water plume in south-west direction. The spatial evolution of pollutants concentrations for hypothetical situations shows patterns influenced directly by the current system.