The interaction of turbulently flowing fluids and porous media occurs in many problems of practical interest. However, the engineering science literature appears to be devoid of either experimental or theoretical studies of such systems. In this paper, extensive flow visualisation experiments and comparisons with computational fluid dynamics (CFD) simulations are reported for these systems. In such systems, the turbulence in the adjacent fluid region can persist in the porous medium depending on its permeability and porosity. In the present study, turbulence is generated by using a round water jet that impinges on a porous foam. Due to the opaque nature of the porous medium, visualisations are carried out only in the fluid layer. However, the flow field in the fluid layer is affected by the flow in the porous medium, especially when the porous foam has a high permeability. Visualisations have been carried out to qualitatively evaluate the effect of the permeability of the porous medium, the height of the fluid layer and the thickness of the porous medium. A mathematical model of the system is formulated which incorporates two different turbulence models and a laminar model for the porous medium. A low-Reynolds number k-epsilon turbulence model is used for the fluid layer in all cases. The resulting CFD predictions reflect well the effects of the changes in the permeability of the porous medium as well as the height of the fluid layer. However, the predictions are not as reliable in showing the changes due to the thickness of the porous medium. Predictions with one of the turbulence models with only Darcy damping in the turbulence transport equations for the porous medium is shown to give better qualitative comparisons for the gross flow patterns. Part II of this paper presents laser Doppler velocimetry measurements for the same system and comparisons of these measurements with the CFD simulations for a quantitative evaluation of the mathematical model.