No / This paper presents an integration procedure for the Reynolds-averaged Navier-Stokes equations for the determination of the distribution of the streamwise velocity using the vertical component. This procedure is dedicated to the outer region and central part of channels. The proposed model is applicable to both rough and smooth flow regimes, provided the velocity at the inner-outer boundary has been properly defined. To generate a simplified expansion, a number of hypotheses are proposed, focusing in particular on the analytical modeling of the vertical component by adopting a negligible viscosity. The proposed hypotheses are validated by the experimental data existing in the literature. The proposed simplified expansion is studied through a sensitivity analysis and proved consistent in regards to model experimental data. The proposed model seems capable of demonstrating different kinds of flows, including dip phenomenon flow patterns.

Yes / The Prandtl second kind of secondary current occurs in any narrow channel flow causing velocity dip in the flow velocity distribution by introducing the anisotropic turbulence into the flow. Here, a study was conducted to explain the occurrence of the secondary current in the outer region of flow velocity distribution using a universal expression. Started from the basic Navier-Stokes equation, the velocity profile derivation was accomplished in a universal way for both smooth and rough open channel flows. However, the outcome of the derived theoretical equation shows that the smooth and rough bed flows give different boundary conditions due to the different formation of log law for smooth and rough bed cases in the inner region of velocity distribution. Detailed comparison with a wide range of different measurement results from literatures (from smooth, rough and field measured data) evidences the capability of the proposed law to represent flow under all bed roughness conditions.

Yes / The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant Br and wake parameter П, where their findings are also compared with values from previous studies. From κ, Br and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, Br and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not. / Major State Basic Research Development Grant 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).

Yes / To reproduce the natural flow topography in a laboratory environment, it is crucial to recapture its bed condition in order to ensure the accurate representation. Water-worked bed represents a state-of-the-art experimentally formed bed to imitate the natural-formed channel in most rivers or natural streams. Recently, this technique has been intensively studied through experimental and computational approaches; however, its actual influence towards the near-bed flow as compared to experimentally prepared rough bed in well-packed bedform order are still yet to be investigated deeply. This experimental study systematically investigated and compared the differences in velocity distribution and three-dimensional (3D) turbulence characteristics, including turbulence intensities and Reynolds stresses, between uniform smooth bed, laboratory-prepared rough bed and water-worked bed open channel flows. The flow comparisons were concentrated at near-bed region where clear flow behaviour change can be observed. Through these comparisons, the study inspected the characteristics of water-worked bedform thoroughly, in order to inform future experimental research that tries to reproduce natural stream behaviours. / the Major State Basic Research Development Grant No. 2013CB036402 from Tsinghua University. The support from the Major State Basic Research Development Program (973 program) of China is also greatly appreciated. We also acknowledge the National Key Research and Development Project from the Ministry of Science and Technology during the Thirteenth Five-year Plan Period (Grant No. 2017YFC0403600) and the Science and Technology Projects State Grid Corporation of China (Grant No. 52283014000T).