Discussion of "transcritical flow due to channel contraction" by O. Castro-Orgaz, J. V. Giraldez, and J. L. Ayuso

The design of channel contraction is not obvious when transcritical or near-critical flows take place. The concept of critical flow conditions was first developed by Bélanger (1828) and later expanded by Bakhmeteff (1912, 1932). Bélanger and Bakhmeteff both defined the concept of critical flow in relation to the singularity of the backwater equation. Herein further applications of transcritical flow in channel contraction are discussed and a solution of the critical flow singularity is presented

Physical Modelling of the Flow Field in an Undular Tidal Bore

A tidal bore may form in a converging channel with a funnel shape when the tidal range exceeds 6-9 m. The advancing surge has a major impact on the estuarine ecosystem. Physical modelling of an undular bore has been conducted based upon a quasi-steady flow analogy. The experimental data highlight rapid flow redistributions between successive wave troughs and crests as well as large bottom shear stress variations. The results suggest a sediment transport process combining scour beneath wave troughs associated with upward matter dispersion between a trough and the following wave crest. The process is repeated at each trough and significant sediment transport takes place with deposition in upstream intertidal zones. The conceptual model is supported by field observations showing murky waters after the bore passage and long-lasting chaotic waves

The known unknowns of hydraulic engineering

Hydraulic engineers and researchers deal with scientific challenges involving turbulent flow motion and its interactions with the surroundings. Turbulent flows are characterised by unpredictable behaviour, and little systematic research has yet been conducted in natural systems. This paper discusses the implications of recent developments in affordable instrumentation previously characterised by intrinsic weaknesses that adversely affect the quality of the signal outputs. A challenging application is the unsteady turbulence field in tidal bores. The interactions between open channel flows and movable boundaries and atmosphere illustrate another aspect of our limited knowledge. Rapid siltation of reservoirs and air entrainment in turbulent free-surface flows are discussed. In both applications, hydraulic engineers require some broad-based expertise. In turn the education of future hydraulic engineers is of vital importance

Development of the Bélanger Equation and Backwater Equation by Jean-Baptiste Bélanger (1828)

A hydraulic jump is the sudden transition from a high-velocity to a low-velocity open channel flow. The application of the momentum principle to the hydraulic jump is commonly called the Bélanger equation, but few know that Bélanger's (1828) treatise was focused on the study of gradually varied open channel flows. Further, although Bélanger understood the rapidly-varied nature of the jump flow, he applied incorrectly the Bernoulli principle in 1828, and corrected his approach 10 years later. In 1828, his true originality lay in the successful development of the backwater equation for steady, one-dimensional gradually-varied flows in an open channel, together with the introduction of the step method, distance calculated from depth, and the concept of critical flow conditions

Environmental Impact of Undular Tidal Bores in Tropical Rivers

A tidal bore impacts significantly on the estuarine ecosystem, although little is known on the flow field, mixing and sediment motion beneath tidal bores. In the absence of detailed systematic field measurements, a quasi-steady flow analogy was applied to investigate undular tidal bores with inflow Froude numbers between 1.25 and 1.6. Experimental results indicated that rapid flow redistributions occur beneath the free-surface undulations, with significant variations in bed shear stress between wave crests and troughs. Dynamic similarity was used to predict detailed flow characteristics of undular tidal bores. The effects of periodic loading on river sediments, scour of river bed and flow mixing behind the bore are discussed. A better understanding of these processes will contribute to better management practices in tidal bore affected rivers, including the Styx and Daly rivers in tropical Australia

Bernoulli theorem, minimum specific energy and water wave celerity in open channel flow

One basic principle of fluid mechanics used to resolve practical problems in hydraulic engineering is the Bernoulli theorem along a streamline, deduced from the work-energy form of the Euler equation along a streamline. Some confusion exists about the applicability of the Bernoulli theorem and its generalization to open-channel hydraulics. In the present work, a detailed analysis of the Bernoulli theorem and its extension to flow in open channels are developed. The generalized depth-averaged Bernoulli theorem is proposed and it has been proved that the depth-averaged specific energy reaches a minimum in converging accelerating free surface flow over weirs and flumes. Further, in general, a channel control with minimum specific energy in curvilinear flow is not isolated from water waves, as customary state in open-channel hydraulics

Free-surface profiles, velocity and pressure distributions on a broad-crested weir: a physical study

Basic experiments were conducted on a large-size broad-crested weir with a rounded corner. Detailed free-surface, velocity, and pressure measurements were performed for a range of flow conditions. The results showed the rapid flow distribution at the upstream end of the weir and next to the weir brink at large flow rates. The flow properties above the crest were analyzed taking into account the nonuniform velocity and nonhydrostatic pressure distributions. Introducing some velocity and pressure correction coefficients, it is shown that critical flow conditions were achieved above the weir crest for 0.1 < x/L-crest < 1. The velocity measurements highlighted a developing boundary layer. The data differed from the smooth turbulent boundary layer theory, although the present results were consistent with earlier studies. On average, the boundary stress was approximately tau(o)/(rho x g x H-1) 0.0015-0.0025. DOI: 10.1061/(ASCE)IR.1943-4774.0000515. (C) 2012 American Society of Civil Engineers

Undular tidal bores: Effect of channel constriction and bridge piers

A tidal bore may occur in a macro-tidal estuary when the tidal range exceeds 4.5-6 m and the estuary bathymetry amplifies the tidal wave. Its upstream propagation induces a strong mixing of the estuarine waters. The propagation of undular tidal bores was investigated herein to study the effect of bridge piers on the bore propagation and characteristics. Both the tidal bore profile and the turbulence generated by the bore were recorded. The free-surface undulation profiles exhibited a quasi-periodic shape, and the potential energy of the undulations represented up to 30% of the potential energy of the tidal bore. The presence of the channel constriction had a major impact on the free-surface properties. The undular tidal bore lost nearly one third of its potential energy per surface area as it propagated through the channel constriction. The detailed instantaneous velocity measurements showed a marked effect of the tidal bore passage suggesting the upstream advection of energetic events and vorticity "clouds" behind the bore front in both channel configurations: prismatic and with constriction. The turbulence patches were linked to some secondary motions and the proposed mechanisms were consistent with some field observations in the Daly River tidal bore. The findings emphasise the strong mixing induced by the tidal bore processes, and the impact of bridge structures on the phenomenon. © 2010 Springer Science+Business Media B.V

Similitude and scale effects of air entrainment in hydraulic jumps

A hydraulic jump is characterised by some strong turbulence and air entrainment in the roller. New measurements were performed in two channels in which similar experiments with identical inflow Froude numbers and relative channel widths were conducted with a geometric scaling ratio of 2:1. Void fraction distributions showed the presence of an advection/diffusion shear layer in which the data followed an analytical solution of the diffusion equation for air bubbles. The data indicated some scale effects in the small channel in terms of void fraction and bubble count rate. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding to lesser overall aeration of the jump roller. Dimensionless bubble count rates were significantly lower in the smaller channel especially in the mixing layer. The study is believed to be the first systematic investigation of scale effects affecting air entrainment in hydraulic jumps using an accurate air-water measurement technique

Unsteady Two-Dimensional Orifice Flow: A Large-Size Experimental Investigation

Orifice flows were used as water clocks since the Antiquity up to the 16-th century. Today orifices and nozzles are used for measuring discharges. Most works were conducted with steady flow conditions and there is little information on the unsteady flow pattern. In this study, the writers describe an experimental investigation of an unsteady orifice flow discharging vertically. The study was conducted in a large-size facility with a rectangular orifice (0.75-m by 0.07-m) discharging up to 1.2 m3 in about 10 seconds. The study presents new information on the unsteady flow patterns, the discharge capacity and the velocity field in the reservoir. The results are compared with 'classical' orifice flow results