Flow Hydrodynamic Characteristics in the Dam-Break Induced Wave Tip Region

Abstract

Traditional models assuming a vertically uniform structure of the horizontal flow velocity and neglecting the vertical velocity distribution cannot accurately describe the complex boundary layer flow features in the dam-break induced wave tip region. Based on the assumption that the horizontal velocity profile in the wave tip region follows a vertically parabolic distribution with shear extending to the water surface, new solutions for the hydrodynamic characteristics in the wave tip region were derived with respect to the simplified force balance or the steady momentum equation, respectively. The force balance-based models show the relation between water depth [Formula: see text] and distance from the tip [Formula: see text] in the wave tip region as [Formula: see text], whereas a complex and implicit [Formula: see text] relation is confirmed after applying the momentum equation. Comparing with other models, the present momentum equation-based model gives the best agreements with experiments, which can illustrate the general spatial distribution of the wave profile in the wave tip region. Model predicted characteristics of surface particles’ motion are consistent with the experimental observation of Baldock et al. ([ 2014 ] “Flow convergence at the tip and edges of a viscous swash front — experimental and analytical modeling,” Coast Eng. 88, 123–130). As for the vertical velocity distribution in the wave tip region (being downward direction), it increases monotonically from the bed to the water surface and its magnitude increases when approaching the wave tip. Taking into account the relative streamline distribution and total flow field feature in the wave tip region, the present model can reproduce the uniform flow convergence pattern at the wave tip front, as experimentally observed in Baldock et al. [ 2014 ].