## 4 Conclusions  
A reasoned comparison between Delft3D-Flow and ROMS was carried out with the aim of evaluating the behaviour of such models in agreement with the turbulence models implemented, especially as far as at the bed velocities and stresses are concerned. Two benchmarks were considered: the first one was a uniform open-channel flow whose logarithmic velocity profile can be derived analytically, whereas the second one was a wind driven circulation in a closed basin induced by a steady wind. The former case was well suited to evaluate the agreement of the model with expected theoretical results, while the latter was taken into consideration since it allowed us to validate the performance of turbulence closures at the varying of the ratio between bed and surface stresses. A degree of variability in the results can be expected, especially adopting closures usually implemented in different contexts. For example, _MY_25 model implemented in ROMS is also much used in atmospheric models such as WRF (weather research and forecasting model) [40] for stratified environments. However, concerning coastal and estuarine environments, such a model should not be used, as the first benchmark clearly demonstrates. Besides, this benchmark provides a useful indication on which model should be adopted in these areas. The profiles of longitudinal velocity obtained with algebraic and \(k-L\) models of Delft3D follow the analytical solution even at lower layers close to the bed. On the other hand, \(k-\epsilon\) model of Delft3D is ill-behaved because does not manage to reproduce the theoretical result at the bottom. Therefore, the bed stresses computed by the models can be accepted only for algebraic and \(k-L\) turbulence closures. As far as ROMS is concerned, \(k-\epsilon\) and \(k-\omega\) models provide acceptable results in terms of bed stresses (see Table 4). Excluding the bottom layer, \(k-\omega\) model follows the rough wall law up to the surface. Indeed, none of the models tested provided an acceptable velocity profile at the bottom. The second benchmark is well-suited to evaluate the variability in the results, discarding possible influences of open boundaries. The variability is quite widespread, as depicted in Figure 9, and this must be kept in mind in case sediment transport should be evaluated. Besides, the behaviour of the models in this benchmark opposed that of the first one. Here, algebraic and \(k-L\) models did not manage to reproduce the inversion of the flow in the central part of the basin, as depicted in Figure 6.  
In conclusion, this work clarifies that in open channel flows, typical of riverine and estuarine areas, algebraic and one-equation models should be preferred to two-equation models. On the contrary, in the presence of strong gradients and flow reversals, two-equation models manage to provide much more realistic results despite the patterns of bed shear stresses not being in complete agreement. Further studies will be devoted to develop better boundary conditions for two-equation models that can overcome the issues reported here. A possible solution would be to apply in \(k-\omega\) models, the conditions proposed by [41] alongside a stretching of the \(\sigma-\)layers that emphasises the refining at the bottom layers. A useful stretching is reported in [31]. Besides, in two-dimensional (2D) shallow-water models the quadratic dependence of stresses from velocity through a conductance coefficient, \(\tau=C\mathbf{U}|\mathbf{U}|\), should be used with care since it cannot reproduce the behaviour of Figure 9.  
All authors contributed to the building of this paper in its different aspects. Conceptualisation: S.P., F.E. and A.S.; methodology: S.P., F.E., G.B., A.C., L.C., M.C. and A.S.; software: S.P., F.E. and A.S.; validation: S.P., F.E., G.B., A.C. and A.S.; formal Analysis: S.P., F.E., G.B., A.C. and A.S.; writing--original draft preparation: S.P., F.E., G.B., A.C., L.C., M.C. and A.S.; writing--review and editing: S.P., F.E., G.B., A.C., L.C., M.C.