Effects of Nonlinearity on Velocity, Acceleration and Pressure Gradient in Free-Stream Zone of Solitary Wave over Horizontal Bed—An Experimental Study

Abstract

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.