Related papers: Continuous hydraulic jumps in laminar channel flow
In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic…
Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froude number F < 2, we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin-film…
We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular this yields the structure of stationary hydraulic jumps, both in their circular and linear versions,…
When a fluid jet strikes an inclined solid surface at normal incidence, gravity creates a flow pattern with a thick outer rim resembling a parabola and reminiscent of a hydraulic jump. There appears to be little theory or experiments…
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…
In this paper, we propose an analytical framework for internal hydraulic jumps. Density jumps or internal hydraulic jumps occur when a supper critical flow of water discharges into a stagnant layer of water with slightly different density.…
The properties of a standard hydraulic jump depend critically on a Froude number Fr defined as the ratio of the flow velocity to the gravity waves speed. In the case of a horizontal circular jump, the question of the Froude number is not…
Hydraulic jumps are oftentimes encountered in natural and human-made environments. The transition from supercritical to subcritical flow involves large energy dissipation rates and substantial air entrainment, preventing the use of…
We carry out an analytical study of laminar circular hydraulic jumps, in generalized-Newtonian fluids obeying the two-parametric power-law model of Ostwald-de Waele. Under the boundary-layer approximation we obtained exact expressions…
We present the results of some experiments on the circular hydraulic jump in normal and superfluid liquid helium. The radius of the jump and the depth of the liquid outside the jump are measured through optical means. Although the scale of…
By reduction to a generalized Sturm Liouville problem, we establish spectral stability of hydraulic shock profiles of the Saint-Venant equations for inclined shallow-water flow, over the full parameter range of their existence, for both…
The formation of a planar hydraulic jump has been analysed in the framework of a full depth-averaged thin film model (DAM) with surface tension effects included. We have demonstrated regular weak solutions of the full DAM and analysed…
We study by a combination of analytical and numerical methods multidimensional stability and transverse bifurcation of planar hydraulic shock and roll wave solutions of the inviscid Saint Venant equations for inclined shallow-water flow,…
Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to…
We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard et al., based on the known flow structure for the type II hydraulic jumps with a "roller" (separation eddy) near the free surface in the jump…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
The flow of viscoelastic fluids in channels and pipes remain poorly understood, particularly at low Reynolds numbers. Here, we investigate the flow of polymeric solutions in straight channels using pressure measurements and particle…
We impose a linearized Eulerian perturbation on a steady, shallow, radial outflow of a liquid (water), whose local pressure function includes both the hydrostatic and the Laplace pressure terms. The resulting wave equation bears the form of…
We consider a special type of hydraulic jumps (internal bores) which, in the vertically bounded system of two immiscible fluids with slightly different densities, conserve not only the mass and impulse but also the circulation and energy.…
Hydraulic jumps in thin films are traditionally explained through gravity-driven shallow-water theory, with surface tension assumed to play only a secondary role via Laplace pressure. Recent experiments, however, suggest that surface…