The water cushion depth of stilling basin with shallow-water cushion is a key factor that 13 affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the 14 water cushion is considered as “shallow” has not be stated clearly for now, and only conceptual 15 description is provided. This paper attempts to specify the best water cushion depth based on the 16 flow...

Local scour around a cylindrical pier in a channel with an erodible bed or natural bed is a common problems in bridge or pile supported structure. The highly unsteady complex flow field around a circular pier produces scour hole mainly for the presence of vortices. The main mechanism that drives the formation and evolution of the scour hole around bridge pier is horse shoe vortex motion. In the...

A hydraulic jump is a sudden, rapid transition from a supercritical flow to a subcritical flow. At large inflow Froude numbers, the jump is characterized by a significant amount of entrained air. For this paper, the bubbly two-phase flow properties of steady and strong hydraulic jumps were investigated experimentally. The results demonstrate that the strong air entrainment rate and the depth-av...

The authors explore the theoretical and empirical relationship between the nonlocal quantities of the entrainment ratio E, the appropriately depthand time-averaged flux coefficient G, and the bulk Froude number Fro in density currents. The main theoretical result is that E 5 0.125 G Fr 2 o(C 3 U /CL)/cosu, where u is the angle of the slope over which the density current flows, CL is the ratio t...

Self-similarity has been the paradigmatic picture for the pinch-off of a drop. Here we will show through high-speed imaging and boundary integral simulations that the inverse problem, the pinch-off of an air bubble in water, is not self-similar in a strict sense: A disk is quickly pulled through a water surface, leading to a giant, cylindrical void which after collapse creates an upward and a d...

We present an asymptotic preserving (AP), large time-step scheme for the shallow water equations in the low Froude number limit. Based on a multiscale asymptotic expansion, the momentum fluxes are split into a nonstiff and a stiff part. A semi-implicit discretisation, where the nonstiff terms are treated explicitly and stiff terms implicitly in time, is crucial to achieve the AP property. A com...