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Modeling wave–current bottom boundary layers beneath shoaling and breaking waves

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Abstract

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant No. 50979033), the Program for New Century Excellent Talents in University of China (NCET-07-0255), and the Special Research Funding of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 2009585812). The authors thank two anonymous reviewers for their valuable comments that have improved the quality of the paper.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, 1 Xikang Road, Nanjing, 210098, China

    Chi Zhang & Jinhai Zheng

  2. Key Laboratory of Coastal Disaster and Defence of Ministry of Education, Hohai University, 1 Xikang Road, Nanjing, 210098, China

    Yigang Wang

  3. U.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, 3909 Halls Ferry Road, Vicksburg, MS, 39180, USA

    Zeki Demirbilek

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  1. Chi Zhang
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  2. Jinhai Zheng
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Correspondence to Jinhai Zheng.

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Zhang, C., Zheng, J., Wang, Y. et al. Modeling wave–current bottom boundary layers beneath shoaling and breaking waves. Geo-Mar Lett 31, 189–201 (2011). https://doi.org/10.1007/s00367-010-0224-9

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