Numerical and experimental turbulence studies on shallow open channel flows

• A numerical model combining the shallow water model with k-ε equations is proposed.
• Improved numerical source terms representation using the SGUM approach is used.
• Experiments are conducted over the smooth/rough beds on uniform/non-uniform flows.
• We conduct study on TKE conditions of different uniform and non-uniform flows.
• Simulations and measurements are compared in flow velocity, TKE and power spectrum.

The standard shallow water equations (SWEs) model has been 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 SWEs k-ε 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 with 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 in the investigated flows.