On Bore Dynamics and Pressure: RANS, Green-Naghdi, and Saint-Venant Equations

Abstract

Propagation and impact of two- and three-dimensional bores generated by breaking of a water reservoir is studies by use of three theoretical models. These include the Reynolds-averaged Navier–Stokes (RANS) equations, the level I Green-Naghdi (GN) equations, and the Saint-Venant (SV) equations. Two types of bore generations are considered, namely, (i) bore generated by dam-break, where the reservoir water depth is substantially larger than the downstream water depth, and (ii) bore generated by an initial mound of water, where the reservoir water depth is larger but comparable to the downstream water depth. Each of these conditions corresponds to different natural phenomena. This study shows that the relative water depth plays a significant role on the bore shape, stability, and impact. Particular attention is given to the bore pressure on horizontal and vertical surfaces. The effect of fluid viscosity is studied by use of different turbulence closure models. Both two- and three-dimensional computations are performed to study their effect on bore dynamics. Results of the theoretical models are compared with each other and with available laboratory experiments. Information is provided on bore kinematics and dynamics predicted by each of these models. Discussion is given on the assumptions made by each model and differences in their results. In summary, SV equations have substantially simplified the physics of the problem, while results of the GN equations compare well with the RANS equations, with incomparable computational cost. RANS equations provide further details about the physics of the problem.