FLOW STRUCTURE IN HYDRAULIC JUMP DURING RUN-DOWN MOTION OF SHOALING SOLITARY WAVE PROPAGATING OVER 1 : 3 SLOPE

The characteristics of vortex structure in the hydraulic jump, which takes place during the run-down motion of a shoaling solitary wave propagating over a 1/3 slope, are investigated experimentally. A flow visualization technique and high speed particle image velocimetry (HSPIV) were used, respectively, for qualitative and quantitative illustrations. Temporal variations of the visualized serial images and the ensemble-averaged velocity fields of the hydraulic jump are demonstrated. Primary concerns are focused on formation of the separated shear layer from the 1:3 slope and on temporal and spatial variations of the vortex structure underlying the unsteady hydraulic jump. Introduction As first observed by Russell (1838), solitary wave propagates with stable motion over a constant waterdepth channel for a long distance. They travel fairly steadily neither steepening their wave height nor widening their effective wave length, but just maintaining constant wave length and wave height. The investigation of shoaling solitary waves can be used to simulate the run-up and run-down motions as well as the shoreward inundation of a tsunami and thus enhance the ability of disaster mitigation for coastal zone. The research for shoaling and run-up of a solitary wave over a slope has been performed by many researchers. A series of experiments was carried out by Synolakis and Skjelbreia (1993) to reveal the amplitude evolution of solitary waves propagating over a sloping bottom. Grilli et al. (1997) studied the characteristics of solitary wave shoaling and breaking on different slopes. A breaking criterion based on the value of a non-dimensional slope parameter was derived. Furthermore, Lin et al. (1999) performed numerical simulations as well as conducted laboratory experiments to study solitary wave run-up and rundown on sloping beaches. Steepand mild-slope beaches were tested, and the consequential nonbreaking and breaking solitary waves were discussed, respectively. Velocity distribution and freesurface profiles resulted from the numerical model were verified with particle image velocimetry (PIV) measurements on the steep-slope case; however, only numerical simulations were performed on the mild-slope case. Li and Raichlen (2002) presented a numerical model for the run-up of non-breaking and breaking solitary waves propagating over a uniform slope. The process of wave breaking and ©Chang Lin, 2015 subsequent post-breaking condition in terms of bore motion were studied by Jensen et al. (2003), depicting experimental study of wave run-up of high solitary waves on a steep slope. In addition, Li and Raichlen (2003) performed experiments to explore the plunging breaking solitary waves as well as the associated bore structure and run-up. Recently, Zhang and Liu (2008) numerically investigated the dynamic process of bore formed by dam-break mechanism in a constant water depth and then traveling over a uniform slope. Sumer et al. (2011) presented two parallel experiments (with rigid-bed and sediment-bed conditions) in connection to the evolution and run-up of plunging solitary waves propagating over a sloping bottom. The experiments showed that the whole sequence of the plunging solitary wave consists of the following processes: wave shoaling and then breaking, run-up, rundown and hydraulic jump, and trailing wave. Employing PIV and wave gauges, Salevik et al. (2013) studied the characteristics of free surface elevation and velocity field of the run-up of solitary waves on a straight slope and a composite beach, respectively. Utilizing PIV and non-intrusive acoustic wave gauge, Pedersen et al. (2013), exhibited very informative data of temporal velocity profiles in the boundary layer during the run-up and rundown stages of a shoaling solitary wave propagating over a 10 sloping bed. However, the velocity measurements by PIV were only conducted at two small areas from the equilibrium shoreline, respectively. Moreover, Lin et al. (2014a) displayed the newest measurement results concerning the velocity fields of shoaling solitary wave in the prebreaking zone and near breaking point, using flow visualization technique and HSPIV. Main concerns were targeted at the near-bottom and boundary-layer flows on a 1/10 slope. Most of previous studies of the solitary wave propagating over a slope mainly focus on variation of free surface elevation during shoaling as well as run-up and run-down processes, breaker type and breaking index, velocity field in the external flow, the maximum run-up height, and so on. The characteristics of hydraulic jump taking place during the run-down motion of a shoaling solitary wave is still very ambiguous, especially for the case of steeper slope. The systematical measurements has not yet been achieved up to now. In this study, the temporal variations of both free surface elevation and velocity fields of hydraulic jump are presented. Special attention will be paid to the separated shear layer from the sloping bottom as well as the temporal and spatial variations of vortical structure underneath the hydraulic jump. Experimental Setup The experiments were conducted in a glass-walled and glass-bottomed wave flume, having dimensions of 14.0 m long, 0.25 m wide and 0.5 m deep. The wave flume was equipped with a piston-type wave maker at one of its end, which was triggered by a servo motor; while at the other end the wave