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Open AccessArticle

Hydrodynamic Features of an Undular Bore Traveling on a 1:20 Sloping Beach

Department of Civil Engineering, National Chung Hsing University, Taichung City 40227, Taiwan
Vattenfall AB Research and Development, Älvkarleby Laboratory, SE-81426 Älvkarleby, Sweden
Division of Concrete Structures, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
Department of Civil Engineering, KLE Dr. M. S. Sheshgiri College of Engineering and Technology, Angol Main Road, Udyambag, Belgaum, Karnataka 590008, India
Department of Data Science and Big Data Analytics, Providence University, Taichung City 43301, Taiwan
Author to whom correspondence should be addressed.
Water 2019, 11(8), 1556;
Received: 5 June 2019 / Revised: 15 July 2019 / Accepted: 25 July 2019 / Published: 27 July 2019
(This article belongs to the Section Hydraulics)
The hydrodynamic characteristics, including local and convective accelerations as well as pressure gradient in the horizontal direction, of the external stream of an undular bore propagating on a 1:20 sloping beach are experimentally studied. A bore with the water depth ratio of 1.70 was generated downstream of a suddenly lifted gate. A high-speed particle image velocimetry was employed to measure the velocity fields during the run-up and run-down motions. The time series of free surface elevation and velocity field/profile of the generated bore, comprising a pure bore accompanied by a series of dispersive leading waves, are first demonstrated. Based on the fast Fourier transform (FFT) and inverse FFT (IFFT) techniques, the free surface elevation of leading waves and the counterpart of pure bore are acquired separately at a specified measuring section (SMS), together with the uniform horizontal velocity of the pure bore. The effect of leading-wave-induced velocity shift on the velocity profiles of the generated bore are then evaluated at the SMS. To understand the calculation procedure of accelerations and pressure gradient, three tabulated forms are provided as illustrative examples. Accordingly, the relationships among the partially depth-averaged values of the non-dimensional local acceleration, convective acceleration, total acceleration and pressure gradient of the generated/pure bore acquired at the SMS versus the non-dimensional time are elucidated. The trends in the non-dimensional accelerations and pressure gradient of the external stream of generated bore are compared with those of the pure bore. During the run-up motion from the instant of arrival of the bore front to the moment of the peak level at the SMS, continuous decrease in the onshore uniform horizontal velocity, and successive deceleration of the pure bore in the onshore direction are evidenced, exhibiting the pure bore under the adverse pressure gradient with decreasing magnitude. However, the pure bore once ridden by the leading waves is decelerated/accelerated spatially and accelerated/decelerated temporally in the onshore direction during the rising/descending free surface of each leading wave. This fact highlights the effect of pre-passing/post-passing of the leading wave crest on the velocity distribution of generated bore. It is also found that, although the leading waves have minor contribution on the power spectrum of the free surface elevation as compared with that of the pure bore, the leading waves do play an important role on the magnitudes of both accelerations and pressure gradient. The largest magnitude of the acceleration contributed by the leading waves is around 26 times the counterpart contributed by the pure bore. Further, during the run-down motion right after the moment for the peak level of the bore, a linear increase in the magnitude of the offshore uniform horizontal velocity and a constant local acceleration with increasing time are both identified. The partially depth-averaged value of the non-dimensional pressure gradient is equal to a small negative constant (−0.0115) in the offshore direction, indicating that the bore is subject to a constant favorable pressure gradient. View Full-Text
Keywords: undular bore; leading waves; high-speed particle image velocimetry (HSPIV); run-up; run-down; velocity shift; local acceleration; convective acceleration; pressure gradient undular bore; leading waves; high-speed particle image velocimetry (HSPIV); run-up; run-down; velocity shift; local acceleration; convective acceleration; pressure gradient
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MDPI and ACS Style

Lin, C.; Wong, W.-Y.; Kao, M.-J.; Yang, J.; Raikar, R.V.; Yuan, J.-M. Hydrodynamic Features of an Undular Bore Traveling on a 1:20 Sloping Beach. Water 2019, 11, 1556.

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