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.

The unsteady overtopping of barriers by gravity currents and dam-break flows

“…Across the shock, however, the depth approximately doubles during the first passage of the shock across the domain (figure 11 a , b ), becoming substantially weaker after the first reflection due to energy dissipation. As shown by Borden, Meiburg & Constantinescu (2012) for moving shocks and Wood & Simpson (1984) and Lawrence & Armi (2022) for stationary shocks, shocks of this size do not cause substantial mixing, and instead the principal difference between our model and real currents is in the balance of momentum flux in the single layer model (2.3 b ) due to the energy dissipation and inertia in the upper layer. We do not expect this effect to be significant in our case of interest, flows under a deep ambient, but certainly would need to be included if the ambient and current were of a similar depth.…”

Antarctic Bottom Water in the Vema Fracture Zone

“…We found such structure of the flow in several equatorial spillways and in laboratory experiments (Morozov et al., 2021). All isotherms below the 1.8°C isotherm in the region of the spillway deepen forming a hydraulic jump (Lawrence & Armi, 2022; Pratt & Whitehead, 2007; Whitehead et al., 1974). The spreading of isotherms around 4,000 m at stations 52010–52012 is reminiscent of an internal hydraulic jump as observed well above the seafloor of a deep‐ocean ridge (van Haren, 2019).…”

Равновесная Модель Слоя Смешения В Стратифицированной Жидкости: Приложения К Глубоководным Течениям

“…Построены решения, соответствующие обтеканию препятствия с образованием внутреннего гидравлического скачка и области интенсивного перемешивания. Результаты численного моделирования подтверждены сопоставлением с экспериментальными данными [5]. Показано, что модель применима для описания характерных особенностей перемешивания и расщепления потока в глубоководных течениях [1,2].…”