Stationary internal hydraulic jumps

Abstract

This is a theoretical and laboratory study of stationary internal hydraulic jumps. These jumps are rapid transitions between internally supercritical flow, generated by placing a sill on the bed of a horizontal rectangular channel, and internally subcritical flow, generated by installing a downstream contraction. This contraction generates an approximately uniform flow downstream of the jump; thus mimicking barotropically driven two-layer flows, as found in tidally driven flows over underwater sills, and flows over mountain ranges driven by large-scale pressure gradients. Upstream of the jump a train of Kelvin–Helmholtz billows forms on the interface between the layers. Upper layer fluid is entrained into these billows, which are subsequently advected into the lower portion of the jump. These billows are broken down by the turbulence of the jump, and the entrained upper layer fluid is mixed with lower layer fluid. Downstream of the jump the upper layer remains homogeneous, the density step at the interface is weakened, the upper portion of the lower layer is approximately linearly stratified, and the lower portion of the lower layer is undisturbed. This altered density profile is the downstream conjugate state of the jump. When the contraction is narrowed the jump moves upstream and ‘drowns’ part of the train of billows, reducing the amount of entrainment. Thus, while the jump is responsible for mixing fluid from the upper layer into the lower layer, it is the position of the jump relative to the upstream train of billows that determines the amount of entrainment.