The main goal of this thesis is to apply the depth averaged shallow water equations to several free surface flows in which the turbulence modelling and the treatment of wet-dry fronts are of special interest. In this context, four different flows have been studied: the generation, propagation and reflection of shallow waves in a 1D flume, the tidal flow in a coastal estuary, the flow in an open channel with a 90º bend, and the flow in vertical slot fishways. The aim of this work is to investigate, for the considered applications, which flow features can be resolved by a depth averaged model and which features are beyond the capabilities of the equations. In order to do so, a finite volume solver for the 2D-SWE, coupled with several depth averaged RANS turbulence models, has been developed. A depth averaged mixing length model and a k-ε model for shallow waters have been included in the code, and a depth averaged algebraic stress model has been proposed. At the same time experimental data has been used to analyse the characteristics of the flow as well as to compare with the numerical results.