Abstract
An experimental results on the spatio-temporal variation of velocity field and vortex structure, generated from the separated boundary layers on the offshore side of the still-water shoreline, during the run-down process of non-breaking solitary waves over a 1:3 sloping beach are presented. Three waves having the incident wave-height to water-depth ratios (H0/h0) of 0.363, 0.263, and 0.171 were generated in a wave flume. Two flow visualization techniques and high-speed particle image velocimetry were employed. The primary topics and new findings are: (1) Mechanism of the incipient flow separation, accompanied by formation of the separated shear layer from the beach surface, is elucidated under the adverse pressure gradient, using the fine data of velocity measurements very close to the sloping boundary. (2) Occurrence of hydraulic jump subsequently followed by development of the tongue-shaped free surface and projecting jet is demonstrated through spatio-temporal variation in the Froude number. It is confirmed by a change in the Froude number from supercritical to subcritical range as the free surface rapidly rises from the onshore to offshore side. (3) A complete evolution of the primary vortex structure (including the core position, vortex size, and velocity distribution passing through the vortex core) is first introduced systematically, together with the illustration of temporal variation in the topological structure. The non-dimensional shoreward distance of the vortex core section decreases with the increase in the non-dimensional time. However, the non-dimensional size height of the primary vortex increases with increasing non-dimensional time. (4) Two universal similarity profiles for both the wall jet flow and the shear layer flow demonstrate independency of the two similarity profiles of the wave-height to water-depth ratio and the beach slope. The similarity profiles indicate the promising collapse of the data from three previous studies for 1:20, 1:10, and 1:5 sloping beaches.
Highlights
The solitary wave is characterized as a long wave having very stable motion of propagation over constant water depth nearly without changing the wave height and length (Russell [1])
The results demonstrate the satisfactory generation of incident solitary waves by the wave maker
Temporal variation of the critical section having Fr = 1.0 can be summarized for t = 0.921–1.094 s (i.e., T = 10.20–12.11) for Case 1
Summary
The solitary wave is characterized as a long wave having very stable motion of propagation over constant water depth nearly without changing the wave height and length (Russell [1]). Water 2018, 10, 1713 travels over a sloping beach, it shoals and/or steepens, deforms continuously before breaking (but does not break for a non-breaking wave), and subsequently starts to run up shoreward until the maximum run-up height has been reached. After reaching the maximum height along the sloping beach, it begins to run down the slope due to the action of gravity. As the water travels down the slope, the flow depth decreases continuously, making the flow supercritical before meeting the subcritical flow in the deep flow zone with decreasing velocity. In Taiwan, as East and West coastal shorelines have beach slope approximately varying from 1:50 to 1:2 and from 1:1000 to 1:100, respectively, the investigation of solitary waves on sloping beaches receives the upmost importance
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