Hydraulic Jump Research Articles

Discussion of “Transverse Nonuniformity of Air–Water Flow and Lateral Wall Effects in Quasi-Two-Dimensional Hydraulic Jump”

Discussion of “Transverse Nonuniformity of Air–Water Flow and Lateral Wall Effects in Quasi-Two-Dimensional Hydraulic Jump”

Energy dissipation for supercritical flows by using screens in double-wall mode

ABSTRACT In the present study, the performance of the perforated screens in double-wall mode was investigated through laboratory experiments. Screens had circular, square, and triangular shapes of openings with a porosity of 45% per unit depth of the screens. The screens were placed vertically with the first screen placed at a distance of 1.5 m from the sluice gate and second screen at a gap of 25 mm downstream of the first screen. The supercritical flow through the sluice gate collided with the screens and forced hydraulic jump was created in the immediate upstream of the screens. Froude number F1 of the supercritical flows approaching the screens varied from 3.20 to 19.40 in all experiments. The relative energy dissipation between the screens upstream and downstream was more than that of the classical hydraulic jumps. Furthermore, it was found that this relative energy loss in the case of the double screen having different shapes of openings in the screens was marginally more than that of the double screen, both having similar shapes of openings. The value of the downstream Froude number of the screen, F2, varied from 1.01 to 1.91, with an average value of 1.41.

Internal tidal sloshing and a non-linear wave source away from topography

The ocean-interior shows omnipresent internal wave motions whose importance becomes more and more acknowledged for deep mixing across the stable vertical density stratification for heat and suspended matter redistribution. To observationally study vertical propagation variations of internal tides away from a steep topographic slope, a >1-km long mooring with 760 high-resolution temperature sensors was deployed at 2380 m depth halfway Mount Josephine NE-Atlantic Ocean for 4 months. In the lower 150 m above the seafloor, internal waves slosh, become highly non-linear and break vigorously, every tidal cycle. After signal separation using semidiurnal band-pass and harmonic filters, the vertical phase propagation shows: 1. Phase differences of 90° are observed in isotherms and cross-slope currents over typically 600 m in the vertical, 2. Non-linearity is already found in harmonic records that describe 300-m large-scale internal tides, 3. Non-uniform thin-layer stratification causes about 50% of the semidiurnal variance in small-scales, 4. Upward internal tide propagation starts at the top of non-linear wave breaking, 5. Downward propagation from above leading to energy-focusing at 700 m above the ocean-floor and about 700 m below the nearest seamount-ridge generates interior hydraulic jumps during spring tide.

Corner universality in polygonal hydraulic jumps

Experiments show that vertical liquid jet impact on a solid plate creates a hydraulic jump which takes on a stable polygonal shape with sharp corners. The corner shape exhibits a striking universality that is characterized by the radius of curvature and corner angle at the tip, which remains nearly constant over a wide range of flow conditions. Knowledge of the corner angle allows one to determine the global jump shape, as defined by a dimensionless geometry number related to the isoperimetric inequality, thus giving a complete description of the jump shape.

Roller fluctuations of pre-aerated high-Froude-number hydraulic jumps

This work presents an experimental study of the fluctuating properties of hydraulic jump rollers for high-Froude-number and pre-aerated inflow conditions, to investigate the validity of empirical relationships in the literature that are derived typically from experiments for smaller Froude numbers and clear-water approach flows. The jump roller fluctuations are evaluated in terms of the dimensions of the roller surface profile, the fluctuation magnitudes and frequencies of the instantaneous jump toe positions and water elevations, including at the tailwater surface, and the formation frequency and advection velocity of internal vortices in the shear layer. The effects of pre-aeration are found primarily in the length-scale properties such as jump length and surface fluctuation magnitudes, while the time-scale properties such as characteristic frequencies of the unsteady motions are not affected. Extrapolation of existing quantitative prediction of jump roller dynamic properties to high-Froude-number flow conditions should be performed carefully. An assessment of the fluctuating bubble counts within fixed time intervals yields close frequencies between the bubble grouping motions in the shear layer and the jump toe and tailwater wave motions, thus implying possible correlations between the roller surface deformations and air entrainment.

Pre-aerated classic hydraulic jump downstream a partly-stepped chute

ABSTRACT Study of hydraulic jumps following aerated supercritical flow has been limited, although this is a common scenario in stilling basins preceded by open-channel spillways. New experiments were performed in a concrete stilling basin model downstream of a sloping stepped chute, where hydraulic jumps were generated on the horizontal stilling basin bed and characterized by bubbly approach flow with Froude numbers 7.6 and 9.3 and Reynolds numbers in the order of 105. Measurements were focused on the jump toe oscillations, jump roller length, and air–water flow property distributions. Comparison of the results with literature data under non-aerated inflow conditions suggested overall insignificant pre-aeration effects on the investigated air–water flow properties, although some comparative analyses were subject to scale effects. The streamwise evolution of air flux suggested that the pre-entrained air did not intrude deeply into the jet-shear layer beyond 1/5 to 1/3 roller length from the jump toe.

Stream Slope as an Indicator for Drowning Potential at Low Head Dams

With the increasing availability of low head dam inventories for the United States, the next challenge is discovering how to determine what dams pose the greatest risk to public safety, preferably before a death occurs. Submerged hydraulic jumps create the dangerous current that drowns roughly 50 recreationists each year, and high tailwater is a key element in its formation. Using a simplified approach based on the Manning equation, flat downstream slopes can be a predictor of high tailwater. Stream slopes at low head dams in Colorado, Idaho, Indiana, Maryland, New Mexico, North Carolina, and Pennsylvania were collected from the NHDPlus HR, and dams with recorded fatalities were compared to stream slopes at low head dams with no recorded fatalities. Using the Mann–Whitney U test, there was not enough evidence to reject the null hypothesis that there is no statistically significant difference between the two populations. Until more fatality data are compiled and more low head dam locations are verified, individual testing of dams is recommended to establish each respective flow range that is likely to pose a risk to public safety.

The momentum-conserving simulation for shallow water flows in channels with arbitrary cross-sections

The momentum-conserving staggered grid (MCS) scheme to simulate shallow water flows in channels of varying width and topography is revisited in this article. Here, we modify the MCS scheme so that it can be applied to channels of arbitrary cross-section. The scheme is validated using steady analytical solutions for channels with rectangular and trapezoidal cross sections. We found that the method was capable of solving a wide variety of test cases; including subcritical, supercritical and transcritical steady flows and flows with hydraulic jumps. This MCS scheme could handle both steady and unsteady problems. In the implementation of a channel with arbitrary cross sections, the simulation depicts the time-lapse evolution of the water level toward the steady state. These results were consistent with previous findings in the literature. All numerical experiments carried out here demonstrate the merits of the numerical MCS scheme.

Free-surface undulation and velocity turbulence in shallow undular hydraulic jumps

Undular hydraulic jumps and bores occur in coastal and estuarial regions at small approach Froude numbers and introduce non-uniform evolution of hydraulic properties in the flow direction, affecting the transport and deposition of sediment and other materials. This paper reports an experimental study of relatively wide undular hydraulic jumps generated in a 1.4-m-wide flume, characterized by inflow aspect ratio less than 0.06 and no lateral shockwave crossing at the first standing wave crest. General free-surface shape observations were conducted for a range of Froude numbers between 1.5 and 2.9 and Reynolds numbers between 2.5 × 104 and 1.2 × 105, while detailed free-surface and velocity measurements were performed at longitudinal and transverse cross-sections using acoustic displacement meters (ADMs) and an acoustic Doppler velocimeter (ADV), at five Froude numbers from 1.5 to 1.9. The results highlight complicated relationship of the three-dimensional free-surface characteristics with the variation of Froude number, which exhibits different features at the first two waves and at other sequent waves. The velocity data highlighted unique features of turbulent velocity redistribution at the first wave, including the distributions of turbulence intensity and Reynolds shear stresses. Particular focus on the formation of a “quiet water” zone below the upward-deflected mainstream flow was reported, with presence of instantaneous reversing velocities above the channel bed. The flow pattern analysis was facilitated with mean vorticity characterization. The results reflect that the evolution of undular hydraulic jump with increasing Froude number is a process of gradual turbulence localization towards the first standing wave, and the transition to a breaking hydraulic jump is achieved by the formation of a surface roller at the steepened jump front overwhelming the “resistance” of the bottom “quiet water” zone and forcing a change in the main flow path.

Pressões turbulentas na posição de flutuação de pressão máxima em bacias de dissipação por ressalto hidráulico

ABSTRACT Turbulent flow is responsible for a significant portion of damages and failures in dams. This paper sought to introduce novel approaches to the estimation of typical parameters used in the design of stilling basins. The standard deviations of pressure samples of 24 hydraulic jumps were analysed throughout the stilling basin longitudinal centreline, and the positions of maximum pressure fluctuation were identified. Next, mean and extreme pressures occurring at this position were calculated. Finally, these parameters were plotted against the inflow Froude number and curves were adjusted to the data. The position where maximum turbulence of undular, weak and oscillating jumps occurs varies according to the Froude number. Steady and strong jumps are more likely to induce negative pressures on the stilling basin. The findings of this paper broaden the knowledge on which regions of the stilling basin must receive special attention, and on how to minimize the chances of damages.

A Numerical Experiment on the Occurrence of Atmospheric Hydraulic Jump at the Taebaek Mountains Downwind

Large-eddy simulation of the lee-side hydraulic jump at the downwind side of the Taebaek Mountains demonstrates the advection of a warm anomaly and the atmospheric reverse roller of negative vorticity. The lee-side hydraulic jump entrains the upper-level atmospheric air into the lower-level atmosphere. The simulated lee-side hydraulic jump occurs under the following conditions on the effective height <i>ĥ</i> and width <i>â</i> of an obstacle: <i>ĥ</i> ≥ 0.74 for â > 10, which are equivalent to <i>Fr<sub>h</sub></i> ≤ 1.35 for <i>Fr<sub>a</sub></i> < 0 .1, where <i>Fr<sub>h</sub></i> and <i>Fr<sub>a</sub></i> are the Froude numbers defined in terms of the height and width of the obstacle, respectively. In detail, the hydraulic jump occurs when the upwind-side mean wind (<i>U</i>) ≤ 12 ms<sup>- 1</sup> for the buoyancy frequency (<i>N</i>) = 0.009 s<sup>- 1</sup>. The wind speed dramatically increases within the 30-minute period when the hydraulic jump occurs. The stronger upwind causes a warmer anomaly and stronger downslope wind gust. This study situates the atmospheric hydraulic jump phenomenon with regard ro wildfire occurrence, and describes it using the Froude number for the width and height of the obstacle. It is shown that a more vulnerable atmospheric environment can be formed when the hydraulic jump occurs, and the wave-breaking of mountain waves related to the hydraulic jump can be predicted by the Froude number.

Investigating the Pressure Fluctuations of Hydraulic Jump in an Abrupt Expanding Stilling Basin with Roughened Bed

Stilling basins with sudden expansions are one of the energy dissipation structures. In the hydraulic jump, pressure fluctuations cause significant damages in stilling basins by cavity formation, erosion, and vibration. Roughness can also lead to changes of the behavior of stream lines and vortices. Despite the large number of works on the topic, the role of roughness in spatial hydraulic jumps is not yet fully understood. Present research aimed to study the influence of rough bed on pressure fluctuations of S-jump in abrupt expanding stilling basin. Experiments were conducted in a 0.8 m width and 12 m length flume. Channel expansions ratios were 0.33, 0.5, 0.67, and 1 within the range of Froude numbers, 2 to 9.5. The results showed that roughness decreases intensity of pressure fluctuations in an abrupt expansion stilling basin. Additionally, in sudden expanding sections, the energy loss increases, and the intensity of pressure fluctuations decrease due to the formation of lateral vortices. The reduction rate of maximum pressure fluctuation was 27%, 46%, and 58% for expansion ratio of 0.67, 0.5, and 0.33, respectively. The results revealed the clear dependence of these variables on the Froude number and the distance to the hydraulic jump toe. The maximum values of extreme pressure fluctuations occur in the range 0.609 < X < 3.385, where X is dimensionless distance from the toe of the hydraulic jump, which makes it highly advisable to reinforce the bed of stilling basins in this range.

Self‐contained two‐layer shallow‐water theory of strong internal bores

AbstractWe show that interfacial gravity waves comprising strong hydraulic jumps (bores) can be described by a two‐layer hydrostatic shallow‐water (SW) approximation without invoking additional front conditions. The theory is based on a new SW momentum equation which is derived in locally conservative form containing a free parameter α. This parameter, which defines the relative contribution of each layer to the pressure at the interface, affects only hydraulic jumps but not continuous waves. The Rankine–Hugoniot jump conditions for the momentum and mass conservation equations are found to be mathematically equivalent to the classical front conditions, which were previously thought to be outside the scope of SW approximation. Dimensional arguments suggest that α depends on the density ratio. For nearly equal densities, both layers are expected to affect interfacial pressure with approximately equal weight coefficients, which corresponds to . The front propagation velocity for agrees well with experimental and numerical results in a wide range of bore strengths. A remarkably better agreement with high‐accuracy numerical results is achieved by , which yields the largest height that a stable gravity current can have.

Energy dissipation in hydraulic jumps using triple screen layers

In the present study, series of laboratory experiments were conducted to investigate the effectiveness of perforated screens as energy dissipators in mixed triple wall mode in the case of small hydraulic structures. The shapes of openings for each layer of screens were either circular, square or triangular. Every layer of the screen had a porosity of 45% per unit depth of the screen. The experiments were conducted to dissipate the energy for supercritical flows of Froude number F1 ranging from 3.2 to 19.3. The screens were placed vertically with the first screen 1.5 m from the sluice gate and consecutive screen at a gap of 25 mm. The experiments showed that the energy of the supercritical flows can be dissipated effectively by using perforated screens. The difference in energy dissipation between the upstream and downstream of the screen was more significant than the energy dissipation caused by classical hydraulic jumps. Comparing the results of the present study with the previous researchers it is found that the energy loss in case of present study more than the previous researchers. The relative energy loss in the present study was found to be varying from 74 to 94%. The value of the Froude number downstream of the screen, F2, was varying from 1.1 to 1.81, with an average value of 1.35. Tailwater deficit parameter, D, if found to be varying from 0.66 to 0.90.

Performance of Intrusive Phase-Detection Probe with Large Sensor Size in Air-Water Flow Measurement and Application to Prototype Hydraulic Jump Study

Performance of Intrusive Phase-Detection Probe with Large Sensor Size in Air-Water Flow Measurement and Application to Prototype Hydraulic Jump Study

Closure to “Case Study of Prototype Hydraulic Jump on Slope: Air Entrainment and Free-Surface Measurement” by Zhongtian Bai, Ruidi Bai, Rongcai Tang, Hang Wang, and Shanjun Liu

Closure to “Case Study of Prototype Hydraulic Jump on Slope: Air Entrainment and Free-Surface Measurement” by Zhongtian Bai, Ruidi Bai, Rongcai Tang, Hang Wang, and Shanjun Liu

Discussion of “Case Study of Prototype Hydraulic Jump on Slope: Air Entrainment and Free-Surface Measurement” by Zhongtian Bai, Ruidi Bai, Rongcai Tang, Hang Wang, and Shanjun Liu

Discussion of “Case Study of Prototype Hydraulic Jump on Slope: Air Entrainment and Free-Surface Measurement” by Zhongtian Bai, Ruidi Bai, Rongcai Tang, Hang Wang, and Shanjun Liu

Flow Over the Spillway of AlAdhiam Dam Under Gated Condition

The AlAdhaim Dam is located 133 kilometers northeast of Baghdad. It is a multipurpose dam and joints the Iraqi dam system in 2000. It has a storage capacity of 1.5 billion m3. The dam has an ogee spillway with a length of 562 m, a crest level of 131.5 m.a.m.s.l. and a maximum discharge capacity of 1150 m3/s at its maximum storage height of 143 m.a.m.s.l. This research aimed to investigate the hydrodynamics performance of the spillway and the stilling basin of AlAdhiam Dam by using numerical simulation models under gated situations. It was suggested to modify the dam capacity by increasing the dam's storage capacity by installing gates on the crest of the dam spillway. The FLUENT program was used to simulate the flow over the spillway. The free surface was calculated using the volume of fluid (VOF) method. To deal with turbulence, the SST k-ω turbulence model was used. The study showed that the spillway is capable of carrying the designed flood discharge and the modified conditions with negative pressure behind the gate and at some points along the spillway. Hydraulic jumps occur at various distances throughout the plunge pool depending on the incoming velocity in the flip bucket.

Hydraulic Jump Behavior during Filling Process of Cast Start II

This paper presents a 0.25-scale quasi-three-dimensional hydraulic model experiment of transient fluid flow phenomena during continuous casting of steel under solidification. Water cooling is performed at the bottom of the mold, and saturated sodium acetate solution is covered on the spring and particle arrangement at the bottom of the mold/on the dummy bar to simulate the solidification phenomenon in the actual continuous casting process. The results show that the solidification on the dummy bar surface is very important to the early stage of the filling process and cannot be ignored. Its influence gradually decreases with the rise of the liquid level, and basically disappears when the liquid level rises to a certain height (steady liquid level, SLL). In SLL, the interface morphology of the solidified layer is more affected by the flow, while the interface morphology of the solidified layer has no significant effect on the liquid surface velocity.

Lock-exchange problem for Boussinesq fluids revisited: Exact shallow-water solution

An exact solution to the lock-exchange problem, which is a two-layer analogue of the classical dam-break problem, is obtained in the shallow-water (SW) approximation for two immiscible fluids with slightly different densities. The problem is solved by the method of characteristics using analytic expressions for the Riemann invariants. The obtained solution, which represents an inviscid approximation to the high-Reynolds-number limit, is, in general, discontinuous containing up to three hydraulic jumps which are due to either multivaluedness or instability of the continuous SW solution. Hydraulic jumps are resolved by applying the Rankine–Hugoniot conditions for the SW mass and generalized momentum conservation equations. The latter contains a free parameter α which defines the relative contribution of each layer to the interfacial pressure gradient. We consider a solution for α=0, which corresponds to both layers affecting the interfacial pressure gradient with equal weight coefficients. This solution is compared with the solutions resulting from the application of the classical Benjamin's front condition as well as the circulation conservation condition, which correspond to α=−1 and α→∞, respectively. The SW solution reproduces all principal features of 2D numerical solution for viscous fluids. The gravity current speed is found to agree well with experimental and numerical results when the front acquires the largest stable height which occurs at α=5−2. We show that two-layer SW equations for the mass and generalized momentum conservation can describe interfacial waves containing hydraulic jumps in a self-contained way without external closure conditions.