A RANS numerical study of experimental swash flows and its bed shear stress estimation
Introduction
The swash zone covers the region of wave run-up and run-down on beaches and coastal structures [2]. Field observation indicated that the swash zone is an important sediment transport area [11,15,21]: the near bottom sediment concentration may be two to three orders of magnitude higher than that in the surf zone, up to 100 kg/m3, and the amount of sediment transported by a single uprush process can reach 10 kg/m. The bed shear stress is not only a representative hydrodynamic parameter, but also a common input parameter in empirical relations of sediment transport [13,14,16]. However, its quantification in the swash zone is subject to uncertainty due to the very shallow water, complex flow structure and the strong unsteadiness.
Conley and Griffin [9] applied the hot film probe to measure the bed shear stress in the field, which showed that the peak uprush bed shear stress was about twice of the peak backwash bed shear stress. Barnes et al. [4] used the shear plate to measure the bed shear stress in laboratory. They mentioned that the flow was mixed with a large amount of air at the time of bore arrival and the water depth was very shallow at the end of the backwash. A commonly used method to estimate the bed shear stress in the swash zone is the log-law method. In particular, by assuming an empirical value for the bed roughness height and using the measured horizontal velocity in a near-bed position, the bed shear stress was often obtained from the log-law description of the vertical distribution of the horizontal velocity (e.g., [10,25]). This method is referred to as the one-position log-law method. By ‘one-position’, it means horizontal velocity of only one near-bed position is used. There are two variants of the log-law method: the depth-averaged variant, and the two-position variant. By the depth-averaged variant, the depth-averaged log-law description is used with an empirical value for the bed roughness height and the depth-averaged horizontal velocity. By the two-position log-law method, one does not have to assume an empirical value for the bed roughness. Instead, measured horizontal velocities at two near-bed positions are substituted into the log-law expression to find solutions for both the bed shear stress and the bed roughness height. It remains unknown which variants can give better or comparable estimations in the swash zone. This concern is motivated by a comprehensive assessment of Wilcock [29], which showed that the depth-averaged version of the log-law method is most suitable for open-channel flows. Moreover, the bed shear stress can also be expressed through the near-bed Reynolds stress, where viscous stress is negligible. Actually, Kikkert et al. [18] have used the Reynolds stress method to calculate the bed shear stress based on the measured data. They pointed out that the method can calculate the bed shear stress in the uprush stage, but there is a lag in time compared with the other methods in the backwash stage. In this paper, the different methods of calculating bed shear stress in the swash zone are compared and their applicability is discussed.
Physically, the bed shear stress refers to the friction produced between the water body and the bed surface. To understand the bed shear stress of the swash zone, it is necessary to analyze the flow structure, which can be obtained by vertical-resolving models. Briganti et al. [7] compared a variety of numerical models for the swash zone, including LES model, RANS model, etc. It was shown that both LES model and RANS model could well reproduce the swash processes. For turbulence simulation of swash flows, LES model was more suitable for surface region, whereas the RANS model could give better results for the near-bed region. Torres-Freyermuth et al. [27] used the 2D RANS model to simulate the experimental swash and found that the bed shear stress in the seaward area was larger than that in the landward area. Pintado‐Patiño et al. [24] used the 2D Volume-Averaged Reynolds-Averaged Naiver-Stokes (VARANS) model to analyze the boundary layer dynamics in the swash zone.
In this study, performances of the above-mentioned methods for calculating bed shear stress in the swash zone are discussed with detailed numerical solutions from a Reynolds-Averaged Navier-Stokes model [19]. A brief description of the concerned experimental dam-break flow generated swash processes and the mathematical formulations for the RANS model are presented in Section 2. In Section 3, simulation results are compared to experimental data and previous knowledge of swash flows. Afterwards, four methods for bed shear stress estimation are summarized in Section 4.1 and are evaluated in Section 4.2 using the simulated vertical flow structure as input data. This paper is concluded in Section 5.
Section snippets
The concerned swash experiment
The dam-break flow-generated swash flows over an impermeable sloping bed [18] are numerically simulated here. The experimental configuration is shown in Fig. 1. A reservoir is set on the left side: the length is 0.983 m; the water depth is 0.6 m; the width is 0.45 m. The water depth downstream of the reservoir is 0.062 m. A slope gradient 1:10 (i.e., bed slope angle ) impermeable fixed slope is set in the downstream of the reservoir. The distance between the slope and the reservoir is
Model-data comparisons
In this section, the validity of the model for simulating swash processes is demonstrated by examining whether the simulation results are consistent with existing understandings of swash hydrodynamics and the available experimental data. The discrepancy between the numerical solutions and the experimental data is quantified by the statistics of the correlation coefficient (r) and the root mean square error (RMSE). They are calculated as follows:
A brief review of the four methods
Four methods for calculating the bed shear stress in the swash zone will be compared, including (1) the three variants of the log-law method; (2) the Reynolds stress method. Besides, the turbulent kinetic energy dissipation rate method can also be used to estimate the bed shear stress indirectly. However, this method requires fluctuation velocity which cannot be obtained by the RANS model, so this one is not compared. According to the log-law, the horizontal velocity along the vertical
Conclusions
In this study experimental dam-break flow generated swash processes are numerically simulated using a RANS model. The applicability of the RANS model to swash flows is demonstrated by good agreements between previous knowledge/measured data and the numerical solutions (i.e., the depth-averaged velocity and water depth, the swash front, the vorticity and the boundary layer thickness). Using numerical solutions as input, four methods for estimating the bed shear stress in the swash zone is
CRediT authorship contribution statement
By Peng Hu: Conceptualization, Methodology, Supervision, Writing - original draft, Writing - review & editing. Jiafeng Xie: Software, Writing - original draft. Wei Li: Supervision, Writing - original draft. Zhiguo He: Supervision, Writing - original draft. Reza Marsooli: Methodology. Weiming Wu: Methodology.
Declaration of Competing Interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research is supported by the National Key Research and Development Program of China (No. 2017YFC0405400), the National Natural Science Foundation of China (Nos. 11772300, 11872332, 11402231), and Zhejiang Natural Science Foundation (No. LR19E090002).
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