Structure of flow in hydraulic jumps
TL;DR: In this paper, a high-speed photographic study was made of the hydraulic jump and it was found that the surface roller was made up of several vortices, which are generated in the early part of the jump and travel downstream.
Abstract: A high-speed photographic study was made of the hydraulic jump. It was found that the surface roller was made up of several vortices. These vortices are generated in the early part of the jump and travel downstream. As they move downstream, they grow by pairing. At the same time, water spills down the steepened surface to replenish the toe and subsequently is rolled up into new vortices. A Fourier analysis of the time series of the toe position indicates a cyclic mechanism, the frequencies of which appear to scale with the upstream velocity and downstream depth.
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TL;DR: In this paper, the results of systematic flume experiments spanning a broad range of supercritical-flow bedforms (antidunes, chutes-and-pools and cyclic steps) developed in mobile sand beds of variable grain sizes are presented.
Abstract: Supercritical-flow phenomena are fairly common in modern sedimentary environments, yet their recognition and analysis remain difficult in the stratigraphic record. This fact is commonly ascribed to the poor preservation potential of deposits from high-energy supercritical flows. However, the number of flume data sets on supercritical-flow dynamics and sedimentary structures is very limited in comparison with available data for subcritical flows, which hampers the recognition and interpretation of such deposits. The results of systematic flume experiments spanning a broad range of supercritical-flow bedforms (antidunes, chutes-and-pools and cyclic steps) developed in mobile sand beds of variable grain sizes are presented. Flow character and related bedform patterns are constrained through time-series measurements of bed configurations, flow depths, flow velocities and Froude numbers. The results allow the refinement and extension of some widely used bedform stability diagrams in the supercritical-flow domain, clarifying in particular the morphodynamic relations between antidunes and cyclic steps. The onset of antidunes is controlled by flows exceeding a threshold Froude number. The transition from antidunes to cyclic steps in fine to medium-grained sand occurs at a threshold mobility parameter. Sedimentary structures associated with supercritical bedforms developed under variable aggradation rates are revealed by means of combining flume results and synthetic stratigraphy. The sedimentary structures are compared with examples from field and other flume studies. Aggradation rate is seen to exert an important control on the geometry of supercritical-flow structures and should be considered when identifying supercritical bedforms in the sedimentary record.
241 citations
Cites background from "Structure of flow in hydraulic jump..."
...2E and F) and trigger even greater turbulence, vorticity and energy dissipation (Long et al., 1991)....
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TL;DR: In this article, a control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number.
Abstract: A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging velocimetry was applied to travelling hydraulic jumps giving centre-plane velocity field images at a frequency of 15 Hz over a Froude number range of 2–6. The mean vorticity determined from these images confirms the control-volume prediction to within the accuracy of the experiment. The flow field measurements show that a strong shear layer is formed at the toe of the wave, and extends almost horizontally downstream, separating from the free surface at the toe. Various vorticity generation mechanisms are discussed.
177 citations
TL;DR: The Oak Ridges Moraine in southern Ontario is a poly-genetic moraine constructed of a number of coalesced deposits of gla- cifluvial and glacilacustrine origin this article.
Abstract: The Oak Ridges Moraine in southern Ontario is a poly- genetic moraine constructed of a number of coalesced deposits of gla- cifluvial and glacilacustrine origin. A detailed study of the facies ar- chitecture has been completed on a series of pit sections extending ; 300 m subparallel to the paleoflow direction. Eight major lithofacies and five facies associations have been described. These data have been interpreted to be upper-flow-regime hyperconcentrated-flood-flow de- posits emplaced under a regime of rapid flow expansion and loss of transport capacity within a plane-wall jet with an associated hydraulic jump. Deposition from the plane-wall jet with jump occurred in three zones of flow transformation: zone of flow establishment, transition zone, and zone of established flow. Massive gravels with unconsolidated sand intraclasts and open-work gravel / gravel-sand couplets were de- posited in the zone of flow establishment by hyperconcentrated and supercritical flows, respectively. Immediately downflow low-angle cross-stratified sand incised by steep-walled scours infilled by diffusely graded sand define the transition zone, the zone of maximum vortex erosion, and the distal limit of deposits emplaced under upper-flow- regime conditions. These strata record rapid bed aggradation from sediment-laden supercritical flows that episodically were scoured by large vortices generated within migrating hydraulic jumps. Strati- graphically upward and downflow strata consist only of lower-flow- regime sedimentary structures. Medium-scale, planar cross-strata and small-scale cross-lamination related to migrating 2-D dunes and cur- rent ripples, respectively, characterize the zone of established flow. The facies and sediment architecture suggest that this fan was deposited during a relatively short period of time (days, weeks) by energetic sed- iment-laden floods.
133 citations
Cites background from "Structure of flow in hydraulic jump..."
...This zone of jet flow is similar to that of a plane-wall jet with flow entrainment of ambient fluid (Long et al. 1991)....
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...A plane-wall jet with jump evolves through three zones of flow development as it penetrates the ambient basin fluid (Long et al. 1991)....
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...Alternatively, scour size and depth may have been linked to the growth in vortex size by streamwise vortex pairing until a single large vortex occupied the complete flow depth (Long et al. 1991)....
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TL;DR: A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number, where both CFD codes had good behavior, but special care is required with swirling flows.
Abstract: A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-e. A Volume Of Fluid (VOF) method is used to track the air-water interface, consequently aeration is modeled using an Eulerian-Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers. Two CFD models: OpenFOAM and FLOW-3D for hydraulic jump in low Reynolds numbers.Representative variables are compared for the two CFD results and experimental data.The model results are also compared to previous studies with good agreement.Both CFD codes had good behavior, but special care is required with swirling flows.A quantification of both models accuracy relating to studied variables is proposed.
131 citations
Additional excerpts
...The first known study reporting turbulence quantities in hydraulic jumps was conducted by Rouse et al. (1959) and was later completed by Rajaratnam (1965) and Long et al. (1991)....
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TL;DR: In this article, the steady front condition for a bore in a two-layer Boussinesq fluid in a channel under the assumption that the energy loss occurs within the contracting layer was derived.
Abstract: According to classical hydraulic theory, the energy losses within an external bore must occur within the expanding layer. However, the application of this theory to describe the propagation of internal bores leads to contradiction with accepted gravity-current behaviour in the limit as the depth of the expanding layer ahead of the bore becomes small. In seeking an improved expression for the propagation of internal bores, we have rederived the steady front condition for a bore in a two-layer Boussinesq fluid in a channel under the assumption that the energy loss occurs within the contracting layer. The resulting front condition is in good agreement with available laboratory data and numerical simulations, and has the appropriate behaviour in both the linear long-wave and gravity-current limits. Analysis of an idealized internal bore assuming localized turbulent stresses suggests that the energy within the expanding layer should, in fact, increase. Numerical simulations with a two-dimensional non-hydrostatic model also reveal a slight increase of energy within the expanding layer and suggest that the structure of internal bores is fundamentally different from classical external bores, having the opposite circulation and little turbulence in the vicinity of the leading edge. However, if there is strong shear near the interface between layers, the structure and propagation of internal jumps may become similar to their counterparts in classical hydraulic theory. The modified jump conditions for internal bores produce some significant alterations in the traditional Froude-number dependence of Boussinesq shallow-water flow over an obstacle owing to the altered behaviour of the upstream-propagating internal bore.
124 citations
References
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TL;DR: In this article, Spark shadow pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainedment rates, and large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle.
Abstract: Plane turbulent mixing between two streams of different gases (especially nitrogen and helium) was studied in a novel apparatus Spark shadow pictures showed that, for all ratios of densities in the two streams, the mixing layer is dominated by large coherent structures High-speed movies showed that these convect at nearly constant speed, and increase their size and spacing discontinuously by amalgamation with neighbouring ones The pictures and measurements of density fluctuations suggest that turbulent mixing and entrainment is a process of entanglement on the scale of the large structures; some statistical properties of the latter are used to obtain an estimate of entrainment rates Large changes of the density ratio across the mixing layer were found to have a relatively small effect on the spreading angle; it is concluded that the strong effects, which are observed when one stream is supersonic, are due to compressibility effects, not density effects, as has been generally supposed
3,339 citations
TL;DR: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel as mentioned in this paper, where dye is injected between the two streams just before they are brought together, marking the vorticitycarrying fluid.
Abstract: A mixing layer is formed by bringing two streams of water, moving at different velocities, together in a lucite-walled channel. The Reynolds number, based on the velocity difference and the thickness of the shear layer, varies from about 45, where the shear layer originates, to about 850 at a distance of 50 cm. Dye is injected between the two streams just before they are brought together, marking the vorticity-carrying fluid. Unstable waves grow, and fluid is observed to roll up into discrete two-dimensional vortical structures. These turbulent vortices interact by rolling around each other, and a single vortical structure, with approximately twice the spacing of the former vortices, is formed. This pairing process is observed to occur repeatedly, controlling the growth of the mixing layer. A simple model of the mixing layer contains, as the important elements controlling growth, the degree of non-uniformity in the vortex train and the ‘lumpiness’ of the vorticity field.
1,335 citations