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For solitary waves on a horizontal bed, the study deals experimentally with the high ratio of wave height (H0) to still water depth (h0) that amplifies the wave nonlinearity. The value of H0/h0 tested in a wave flume ranges from 0.050 to 0.550, indicating the shift from a quasi-linear solitary wave to a highly nonlinear one. A high-speed particle image velocimetry (HSPIV) and a flow visualization technique of particle-trajectory tracking method are utilized to measure velocity fields and identify near-bed flow structures. The unsteady free-stream velocities with equal magnitude take place in a free-stream zone, FSZ). The FSZ underlies the internal flow zone, over which the external free surface of solitary wave exists and is situated beyond the boundary layer. The spatio-temporal variation of free-stream velocity, moving in phase with the free surface elevation, characterizes the pattern of pressure gradient in the FSZ and thus dominates the behavior of boundary layer flow. Accordingly, nonlinear effects on the time series as well as the maximum values of horizontal velocity, particle acceleration, and pressure gradient in the FSZs of solitary waves are presented. Before, at, and after the wave crest's intersection with a given measurement location, favorable, zero, and adverse pressure gradients occur in the FSZ, respectively. For H0/h0 = 0.179, 0.363, and 0.550, the values of the dimensionless maximum free-stream velocity are about 3.10, 5.32, and 6.20 times that (= 0.0473) for H0/h0 = 0.050; and the corresponding values of the dimensionless maximum adverse pressure gradient are about 5.74, 14.54 and 19.84 times that (= 0.0061) for H0/h0 = 0.050. This evidence highlights the nonlinear effect on the kinematic and hydrodynamic features of solitary waves. Finally, the effect of nonlinearity on the relationship between the dimensionless time for the maximum adverse pressure gradient in the FSZ and that for the incipient flow reversal in the bottom boundary layer is explored for the first time. It is found that the incipient flow reversal takes place immediately after the maximum adverse pressure gradient, together with a decrease in the dimensionless time for flow reversal if H0/h0 increases. The fact accentuates the nonlinear effect on the incipient flow reversal right above the bed. [ABSTRACT FROM AUTHOR]

This study presents experimental data on the hydrodynamic features of a nonlinear solitary wave of height H0 = 2.9 cm propagating over a horizontal bed in otherwise still water depth h0 = 8.0 cm. High-speed particle image velocimetry is used to quantify the local and convective particle accelerations and pressure gradients under the solitary wave. It is found that the magnitudes of the horizontal and vertical particle local accelerations are invariably larger than their convective counterparts, highlighting the important contribution of local acceleration to the pressure gradient in a solitary wave. The dimensionless pressure gradient in the horizontal direction is favorable, zero, and adverse for time before, at, and after the wave crest passes the section of interest. The dimensionless adverse pressure gradient exhibits a maximum for the dimensionless time T[=t(g/h0)1/2, where g is the gravitational acceleration and t is the time with respect to the crest passing the section] = 1.39, at which the dimensionless local acceleration has a negative maximum. Subsequently, flow reversal takes place above the bed surface. The relationship is elucidated between flow reversal at the bed surface and the evolution of the adverse pressure gradient in the near-bed zone, where uniform horizontal/free stream velocity exists. [ABSTRACT FROM AUTHOR]

This study investigates experimentally similarity and Froude number similitude (FNS) in the dimensionless flow features of three solitary waves traveling on a 1:3 sloping beach. These three waves, designated as cases A, B, and C, respectively, have different heights H0 (=5.8 cm, 2.9 cm, and 1.815 cm) and still water depths h0 (=16.0 cm, 8.0 cm, and 5.0 cm), but identical ratios H0/h0 (=0.363). A high-speed particle image velocimetry system is employed to obtain the free surface profiles (FSPs) and velocity fields/profiles. These features include the free surface elevation (FSE)/FSP time series; velocity fields and profiles, positions, and propagation speeds of flow demarcation curves; times and maximum onshore distances of the maximum run-up heights (MRHs); and times and onshore distances of hydraulic jumps for cases A and B. When the swash tip of a solitary wave reaches the MRH, the contact point becomes almost immobile for a short time interval, with the contact angle changing from obtuse, via right, to acute angle. For cases A and B, the similarities in the dimensionless MRHs and times, at which the run-down motions of the wave tips start, are affirmed. These facts highlight that the swash tips and contact points are subject to complex interactions among gravity force, viscous friction, and surface tension of fluid. Case C, having the smallest length scale, is only focused on the arrival or starting time of the MRH or run-down motion and the MRH and used as a counterexample to demonstrate the absence of similarity or FNS due to the relatively prominent effects of viscous friction and surface tension. [ABSTRACT FROM AUTHOR]

This paper presents experimental results regarding the existence of similarities and/or Froude number similitudes in the time series of the free-surface elevation (FSE) and horizontal velocity of undular bores (UBs) propagating over a horizontal bed. Two wave gauges and high-speed particle image velocimetry are employed to measure the FSEs and velocity fields. A complete evolution of the FSE (or horizontal velocity) of UBs is divided into four temporal stages, named stages I–IV. The surge-wave amplitudes, constant characteristic horizontal velocities, and specified time differences are then identified as the characteristic length scale, velocity scale, and timescale of UBs. Data for the dimensionless FSE and free-stream velocity vs the dimensionless shifted time are found to collapse onto two unique similarity trends. This demonstrates the existence of Froude number similitudes for the entire evolution of UBs with geometric similarity. Under the same water-depth ratio and length ratio, but distinct values of the relative basin and travel length for different UBs, larger values of the relative basin length produce greater end times for the final occurrence of the constant FSE and characteristic horizontal velocity. This demonstrates that the end time is not influenced by the relative travel length. Under identical values of the water-depth ratio and relative basin length, a smaller relative travel length results in a greater rate of decrease in the unit discharge during stage IV. Correspondingly, this results in earlier bifurcation of the time series of FSE (or free-stream velocity), which has a smaller (or larger) rate of decrease, from their counterparts with larger relative travel lengths. [ABSTRACT FROM AUTHOR]

Experimental results are presented regarding the free-surface elevations, velocity fields, and horizontal pressure gradients of dambreak-generated undular bores propagating over a horizontal bottom. Ultrasonic wave gauges, high-speed particle image velocimetry, and a flow visualization method are used to investigate the flow fields. Features of the full-depth velocity field and pressure gradient (equal to minus the sum of the local and convective accelerations) in the free stream over the boundary layer are elucidated with respect to the phase of the free-surface elevation and are categorized into four temporal stages. For stage I with rising free-surface elevations, a successive increase in the magnitude of the pressure gradient (with a negative value) corresponds to a favorable pressure gradient in the free stream. Around the zero-up/down-crossing phase of each leading wave evolving in stage II, the pressure gradient has a negative/positive maximum, revealing the maximum favorable/adverse pressure gradient in the free stream. However, the pressure gradient is zero at each crest or trough phase, showing an instantaneous zero pressure gradient. Within stage III characterized by a constant free-surface elevation, the pressure gradient is almost zero. In stage IV with descending free-surface elevations, the pressure gradient first increases from nearly zero to a positive maximum (representing the maximum adverse pressure gradient), then keeps this value for a period of time, and eventually decreases to zero. Subsequently, flow reversal with an increase in thickness over the bottom and free-stream velocity equal to zero takes place. [ABSTRACT FROM AUTHOR]

This study presents, experimentally, similarity and Froude number similitude (FNS) in the dimensionless features of two solitary waves propagating over a horizontal bed, using two wave gauges and a high-speed particle image velocimetry (HSPIV). The two waves have distinct wave heights H0 (2.9 and 5.8 cm) and still water depths h0 (8.0 and 16.0 cm) but identical H0/h0 (0.363). Together with the geometric features of free surface elevation and wavelength, the kinematic characteristics of horizontal and vertical velocities, as well as wave celerity, are elucidated. Illustration of the hydrodynamic features of local and convective accelerations are also made in this study. Both similarity and FNS hold true for the dimensionless free surface elevation (FSE), wavelength and celerity, horizontal and vertical velocities, and local and convective accelerations in the horizontal and vertical directions. The similarities and FNSs indicate that gravity dominates and governs the wave kinematics and hydrodynamics. [ABSTRACT FROM AUTHOR]

Abstract For providing new insights into the effect of the leading waves on the velocity distribution of the generated bore, a case study of the undular bore (or weak bore) with the water depth ratio 1.70 is tested in a flume, using flow visualization technique (FVT) and high-speed particle image velocimetry (HSPIV). The undular bore, generated right downstream of a suddenly lifted gate, propagates first over a horizontal bottom and then travels over a 1:20 sloping bottom. The wave gauges were used to measure the free surface elevations of the generated bore at different positions. A complete evolution of the free surface elevations of the generated bore accompanied by the dispersive leading waves, measured at different shoreward positions, is elucidated first. Illustrations of variations in wave period and height of each leading wave in the onshore direction are also made. Based on visualized images and velocity fields measured, the following flow features at different stages of the generated bores are explored: (1) The temporal and spatial variations in the flow field of the generated bore with respect to passing of the leading waves; (2) The influence of the leading waves on shifting of the velocity distribution of the generated bore, along with illustrations of flow acceleration or deceleration in the onshore direction; (3) Flow reversal zone and shear layer formation near the sloping bottom; (4) Development of a vortex train (or street) in the shear layer between two opposite currents consisting of the onshore run-up flow and the offshore flow reversal right over the sloping bottom. [ABSTRACT FROM AUTHOR]