Yes / For the abutment bed scour to reach its equilibrium state, a long flow time is needed. Hence, the employment of usual strategy of simulating such scouring event using the 3D numerical model is very time consuming and less practical. In order to develop an applicable model to consider temporally long abutment scouring process, this study modifies the common approach of 2D shallow water equations (SWEs) model to account for the sediment transport and turbulence, and provides a realistic approach to simulate the long scouring process to reach the full scour equilibrium. Due to the high demand of the 2D SWEs numerical scheme performance to simulate the abutment bed scouring, a recently proposed surface gradient upwind method (SGUM) was also used to improve the simulation of the numerical source terms. The abutment scour experiments of this study were conducted using the facility of Hydraulics Laboratory at Nanyang Technological University, Singapore to compare with the presented 2D SGUM-SWEs model. Fifteen experiments were conducted over a total period of 3059.7 hours experimental time (over 4.2 months). The comparison shows that the 2D SGUM-SWEs model gives good representation to the experimental results with the practical advantage.

Yes / This study uses an improved k –ε coupled shallow water equations (SWE) model that equipped with the numerical computation of the velocity fluctuation terms to investigate the turbulence structures of the open channel flows. We adapted the Kolmogorov K41 scaling model into the k –ε equations to calculate the turbulence intensities and Reynolds stresses of the SWE model. The presented model was also numerically improved by a recently proposed surface gradient upwind method (SGUM) to allow better accuracy in simulating the combined source terms from both the SWE and k –ε equations as proven in the recent studies. The proposed model was first tested using the flows induced by multiple obstructions to investigate the utilised k –ε and SGUM approaches in the model. The laboratory experiments were also conducted under the non-uniform flow conditions, where the simulated velocities, total kinetic energies (TKE) and turbulence intensities by the proposed model were used to compare with the measurements under different flow non-uniformity conditions. Lastly, the proposed numerical simulation was compared with a standard Boussinesq model to investigate its capability to simulate the measured Reynolds stress. The comparison outcomes showed that the proposed Kolmogorov k –ε SWE model can capture the flow turbulence characteristics reasonably well in all the investigated flows. / The Major State Basic Research Development Program (973 program) of China (No. 2013CB036402)

Yes / Based on the previous studies, the shallow water equations (SWEs) model was proven to be insufficient to consider the flow turbulence due to its simplified Reynolds-averaged form. In this study, the k-ε model was used to improve the ability of the SWEs model to capture the flow turbulence. In terms of the numerical source terms modelling, the combined k-ε SWEs model was improved by a recently proposed surface gradient upwind method (SGUM) to facilitate the extra turbulent kinetic energy (TKE) source terms in the simulation. The laboratory experiments on both the smooth and rough bed flows were also conducted under the uniform and non-uniform flow conditions for the validation of the proposed numerical model. The numerical simulations were compared to the measured data in the flow velocity, TKE and power spectrum. In the power spectrum comparisons, a well-studied Kolmogorov’s rule was also employed to complement both the numerical and experimental results and to demonstrate that the energy cascade trend was well-held by the investigated flows. / The Major State Basic Research Development Program (973 program) of China (Grant Number 2013CB036402). Open Fund from the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, China (Grant Number SKLH-OF-1103).