Velocity characteristics in boundary layer flow caused by solitary wave traveling over horizontal bottom

Abstract

The characteristics of horizontal velocity in the bottom boundary-layer flow induced by a solitary wave propagating over a horizontal bottom are presented experimentally, using high-speed particle image velocimetry (HSPIV). The ratio of wave height to water depth varies from 0.096 to 0.386 and the flow inside the boundary layer is laminar. The results show that the horizontal velocity profiles can be mainly classified into two categories with respect to the passing of the solitary wave-crest at the measuring section: the pre-passing (or acceleration) phases under favorable pressure gradient and post-passing (or deceleration) phases under adverse pressure gradient. For the velocity distributions obtained during the pre-passing phases, a nonlinear regression analysis was used to precisely determine the time-dependent characteristic length and velocity scales underlying these profiles. A similarity profile of the horizontal velocity is established first using the time-dependent free-stream velocity and boundary layer thickness as the characteristic velocity and length scales, respectively. In addition, the displacement thickness, the momentum thickness, and the energy thickness are also considered as alternative length scales. All these four representative thicknesses are closely related to each other, demonstrating that any one amongst them can be regarded as the characteristic length scale. The forms of similarity profiles for the non-dimensional velocity distributions are somewhat analogous to the results of steady boundary layer flow over a thin plate under with pressure gradient, but with different coefficients or powers. While during the post-passing phases, flow reversal which acts like an unsteady wall jet and moves in the opposite direction against the wave propagation occurs after the passage of solitary wave-crest. The thickness of flow reversal layer increases with time. A similarity profile is proposed for the velocity distributions corresponding to occurrence of the extreme value in the maximum negative velocity of flow reversal. Variations of the maximum negative velocity and the thickness of flow reversal with the time right after the start of flow reversal are also discussed in detail. Moreover, the non-dimensional time leads of the horizontal velocities at different heights in the boundary layer over the free-stream velocity are evidenced to be more noticeable toward the bottom, and also in lower ratio of wave height to water depth. A similarity profile for the non-dimensional time lead versus the non-dimensional height above the bottom surface is also presented.