The unsteady two-dimensional flow of a viscous incompressible fluid in a rectangular cavity, driven by effects of shear and/or buoyancy, is modelled numerically. This physical problem is studied from the viewpoint of obtaining accurate and efficient numerical solutions to the Navier-Stokes equations, applicable to the simulation of convective exchange processes in stratified water bodies, where flows are driven by forced (wind-induced) and/or natural (buoyancy-induced) convection, e.g. in lakes, ponds and reservoirs. The hydrodynamic model, based on the vorticity-stream function formulation, was found to be highly accurate and economical in obtaining iterative solutions to nonlinear coupled systems for a wide range of Reynolds/ Grashof numbers and height/width cavity ratios that can be encountered in natural environments.