High order simulation models for the resolution of wave propagation phenomena in turbulent free surface flows

A depth-averaged large eddy simulation (DA-LES) model, based on the unsteady Reynolds averaged Navier Stokes approach for the shallow water equations, is herein presented. The simulation model aims at the resolution of free surface shallow flows where large-scale turbulence is mainly two-dimensional. The keystone of the model is the combination of a high order of accuracy in space and time with a suitable turbulence modelling that accounts for the effect of the unresolved eddies in the mean flow. The proposed model ensures the well-balanced property (i.e. quiescent equilibrium with machine precision) thanks to the use of augmented Riemann solvers, which include the bed slope source term in the definition of the derivative Riemann problem. The performance of the proposed model is assessed using experimental data from the literature. In particular, a laboratory experiment involving a shallow water flow over a submerged conical island is considered. The numerical results evidence that the proposed model is able to reproduce transient turbulent phenomena, providing a higher level of information and resolution than other models based on the traditional RANS (Reynolds averaged Navier Stokes) approach.