Peng - Transformation of wave skewness and asymmetry over...

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Transformation of wave skewness and asymmetry over smooth low-crested breakwaters Zhong Peng, Qingping Zou, Baoxing Wang and Dominic Reeve School of Engineering, University of Plymouth, UK Abstract Laboratory data sets of oblique wave transmission over smooth low-crested breakwaters collected in DELOS project were analyzed to investigate the transformation of wave skewness and asymmetry. Our analysis demonstrates that at the incident side, wave skewness and asymmetry exhibit quadratic dependence on Ursell number but are not sensitive to free board and incident wave angle. At the transmission side, wave skewness shows linear dependence on Ursell number and increases with Ursell number more rapidly at a smaller relative free board. Wave asymmetry increases rapidly up to a maximum then decays slowly with Ursell number for negative free boards. Otherwise, wave asymmetry increases approximately linearly with Ursell number. Wave asymmetry changes from negative at the incident side to positive at the transmission side. The effect of incident wave angle on asymmetry is negligible. A set of empirical formulae for wave skewness and asymmetry was established using regression procedures. Predictions are in a good agreement with observations. 1. Introduction Better understanding of wave transformation over the smooth low-crested breakwater (SLCB) is crucial in the assessment of functionality and stability of coastal and flood defence schemes. In addition, it has long been recognized that wave skewness and asymmetry are directly related to sediment transport and subsequent beach morphology. It was observed that the onshore velocity associated with a wave crest was more effective at moving coarse sediment than the offshore velocity associated with a wave trough (Cornish, 1898). This observation was consistent with the theory of Stokes (1847), who predicted the onshore velocity related to a wave crest is larger and of shorter duration than the offshore velocity associated with a wave trough. The lack of symmetry of wave profile relative to horizontal axis is called wave skewness. On the other hand, waves with steep front face and gentle rear face were described as pitch forward waves. The lack of symmetry of wave profile relative to vertical axis is called wave asymmetry, which can be calculated from the skewness of the Hilbert transform of wave time series (Elgar and Guza, 1985). Based on the bispectral analysis of observered data sets for natural beach, Doering and Bowen (1995) proposed empirical relationships of wave skewness and asymmetry with Ursell number. Using evolutionary algorithm, Doering et al. (2000) derived analytical expressions for velocity skewness under shoaling and breaking waves. Their results showed that Ursell number is the most important factor for wave skewness, the formula for wave asymmetry was not proposed in their paper. However, these studies focused on wave skewness and asymmetry on natural beaches, the effect of coastal structures on wave skewness and asymmetry have not been investigated.
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