Turbulent dam-break waves of Newtonian and non-Newtonian fluids

The paper uses three-dimensional large eddy simulation (LES) to investigate the structure and propagation of dam break waves of non-Newtonian fluids described by a power-law rheology. Simulations are also conducted for the limiting case of a dam-break wave of Newtonian fluid (water). Turbulent dam-break waves are found to have a two-layer structure and to generate velocity streaks beneath the region in which the flow is strongly turbulent and lobes at the front. The bottom part of the wave resembles a boundary layer and contains a log-law sublayer, while the streamwise velocity is close to constant inside the top layer. The value of the von Kármán constant is found to reach the standard value (i.e. $\kappa$ ≈ 0.4) associated with turbulent boundary layers of Newtonian fluids only inside the strongly turbulent region near the front of Newtonian dam-break waves. Much higher values of the slope of the log law are predicted for non-Newtonian dam-break waves (i.e. $\kappa$ ≈ 0.28) and in the regions of weak turbulence of Newtonian waves. LES shows that a power-law relationship can well describe the temporal evolution of the front position during the acceleration and deceleration phases, and that increasing the shear-thinning behaviour of the fluid increases the speed of the front. The numerical experiments are then used to investigate the predictive abilities of shallow water equation (SWE) models. The paper also proposes a novel one-dimensional (1-D) SWE model which accounts for the bottom friction by employing a friction coefficient regression valid for power-law fluids in the turbulent regime. An analytical approximate solution is provided by splitting the current into an outer region, where the flow is considered inviscid and friction is neglected, and an inner turbulent flow region, close to the wave front. The SWE numerical and analytical solutions using a turbulent friction factor are found to be in better agreement with LES compared with the agreement shown by an SWE numerical model using a laminar friction coefficient. The paper shows that inclusion of turbulence effects in SWE models used to predict high-Reynolds-number Newtonian and non-Newtonian dam break flows results is more accurate predictions.