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The experimental evaluation of the performance of a corrugated apron under free flow subcritical and submerged conditions was conducted, with a focus on scour patterns over the apron. Comparative analysis with a smooth rigid apron revealed an increase in scour depth upon the application of the corrugated apron under free and submerged jet flow conditions. The implementation of a corrugated apron resulted in a considerable reduction in scour depth and length compared to a smooth rigid apron. The maximum reduction in scour depth and length amounted to 79% and 83%, respectively, while the minimum reduction observed was 13% in scour depth and 11% in scour length. Additionally, investigations into velocity and turbulence characteristics over both smooth and corrugated aprons were conducted. It was observed that the rate of turbulence intensity increase within the scour hole due to the presence of a smooth apron surpassed that of the corrugated apron. Scour downstream of the corrugated apron exhibited distinct delineations, including regions of jet diffusion, transition, acceleration, and a recirculating zone near the bed of the scour hole. [ABSTRACT FROM AUTHOR]

Straits and narrows are the place of intensified turbulent mixing. Deep understanding of the turbulent dynamics at these locations is of crucial importance as it conditions the properties of the water masses flowing in the open ocean. A new extensive field experiment, PROTEVS GIB20, with high frequency measurements has been conducted in the Strait of Gibraltar. It allows us to infer dissipation rates of the turbulent kinetic energy, ϵ, from two consistent methods. The range of ϵ is depicted for the different processes which developed in the vicinity of Camarinal Sill, the main topographic feature of the Strait of Gibraltar. It evidences that the bottom boundary layer, hydraulic jumps and large overturns are the main loci of intensified turbulence reaching 10−3W.kg−1. The variability of the turbulence is mainly controlled by semi‐diurnal, diurnal and fortnightly tidal oscillations. Spatially, the western flank of Camarinal Sill is evidenced as the hotspot for turbulent mixing. We confirm a weak variation of the spatially averaged vertically integrated turbulent dissipation rate. This result needs to be qualified in view of the differentiated impact of the various processes on adjacent water masses. The dynamics of the spring tide directly mix Atlantic and Mediterranean waters, resulting in a large spreading of the T‐S diagram. Plain Language Summary: A recent field experiment, PROTEVS GIB20, was performed in the Strait of Gibraltar in October 2020. This experiment was partly designed to observe the turbulent dynamics of the flow in this region. The Strait of Gibraltar presents an important topographic sill, Camarinal Sill, where the current reaches its maximum value enhancing the turbulent processes. Quantifying the turbulence intensity and the associated mixing that develops there is of crucial importance to understand the impact of small‐scale process on larger/regional scales which is now recognized but remains incompletely understood. Such measurements are necessary to assess the performances of the parametrization use in climate model which to dot represent such small‐scale dynamics. Direct measurements of dissipation rate of turbulent kinetic energy are rare near Camarinal Sill, due to the rough environment and strong maritime traffic. From different methods, we infer time series and spatial averages of the turbulence dissipation rate. We describe the variability of the turbulence, the physical processes involved and the impact on water mass mixing. Key Points: Dissipation rates of TKE are inferred near the Camarinal Sill with maximum values of 10−3 W/kg in the hydraulic jumpThe spatio‐temporal distribution of dissipation rates near Camarinal Sill shows maxima on the western flank in tidal outflowsMixing rates are similar during spring and neap tides except for the Atlantic waters more impacted by spring tide hydraulic jumps [ABSTRACT FROM AUTHOR]

Assessing drag force and Reynolds stresses in turbulent flows is crucial for evaluating the stability and longevity of hydraulic structures. Yet, this task is challenging due to the complex nature of turbulent flows. To address this, physical models are often employed. Nonetheless, this practice is associated with difficulties, especially in the case of high sampling frequency where the inherent randomness of velocity fluctuations becomes mixed with the measurement noise. This study introduces a stochastic approach, which aims to mitigate bias from measurement errors and provide a probabilistic estimate of extreme stress values. To accomplish this, a simple experimental setup with a hydraulic jump was employed to acquire long-duration velocity measurements. Subsequently, a modified first-order autoregressive model was applied through ensemble simulations, demonstrating the benefits of the stochastic approach. The analysis highlights its effectiveness in estimating the uncertainty of extreme events frequency and minimizing the bias induced by the noise in the high-magnitude velocity measurements and by the limited length of observations. These findings contribute to advancing our understanding of turbulent flow analysis and have implications for the design and assessment of hydraulic structures. [ABSTRACT FROM AUTHOR]

The experimental evaluation of the performance of a corrugated apron under free flow subcritical and submerged conditions was conducted, with a focus on scour patterns over the apron. Comparative analysis with a smooth rigid apron revealed an increase in scour depth upon the application of the corrugated apron under free and submerged jet flow conditions. The implementation of a corrugated apron resulted in a considerable reduction in scour depth and length compared to a smooth rigid apron. The maximum reduction in scour depth and length amounted to 79% and 83%, respectively, while the minimum reduction observed was 13% in scour depth and 11% in scour length. Additionally, investigations into velocity and turbulence characteristics over both smooth and corrugated aprons were conducted. It was observed that the rate of turbulence intensity increase within the scour hole due to the presence of a smooth apron surpassed that of the corrugated apron. Scour downstream of the corrugated apron exhibited distinct delineations, including regions of jet diffusion, transition, acceleration, and a recirculating zone near the bed of the scour hole.

This study presents a comprehensive dataset comprising multiple data packages derived from laboratory experiments on steady and unsteady hydraulic jumps interacting with a large-scale Gaussian-shaped bed obstacle in an open-channel flume. The primary objective was to accurately measure the impact of hydraulic jump on the free surface and the bed pressure along the obstacle, ensuring the transferability of the results. A multi-process method was followed: designed experiments were recorded, images were postprocessed, and water level data were digitalized. For steady conditions, the bed pressure along the obstacle were measured by piezometers. The repository data are organized and provided in a single package, supplemented by a second package containing panoramas for each experimental time instant and graphical representations of the data, facilitating rapid evaluation of the outcomes. This study provides versatile data that can be utilized in various ways, particularly for fluvial model validation and studying turbulence-driven phenomena in open-channel flows. The detailed methodology presented herein can contribute to the advancement of enhanced laboratory techniques to study similar flow problems. [ABSTRACT FROM AUTHOR]

A high‐resolution model in conjunction with realistic background wind and temperature profiles has been used to simulate gravity waves (GWs) that were observed by an atmospheric radar at Syowa Station, Antarctica on 18 May 2021. The simulation successfully reproduces the observed features of the GWs, including the amplitude of vertical wind disturbances in the troposphere and vertical fluxes of northward momentum in the lower stratosphere. In the troposphere, ship‐wave responses are seen along the coastal topography, while in the stratosphere, critical‐level filtering due to the directional shear causes significant change of the wave pattern. The simulation shows the multi‐layer structure of small‐scale turbulent vorticity around the critical level, where turbulent energy dissipation rates estimated from the radar spectral widths were large, indicative of GW breaking. Another interesting feature of the simulation is a wave pattern with a horizontal wavelength of about 25 km, whose phase lines are aligned with the front of turbulent wake downwind of a hydraulic jump that occurs over steep terrain near the coastline. It is suggested that the GWs are likely radiated from the adiabatic lift of an airmass along an isentropic surface hump near the ground, which explains certain features of the observed GWs in the lower stratosphere. Plain Language Summary: In this study, a high‐resolution computer model was used to simulate atmospheric gravity waves (GWs) that were observed by an atmospheric radar in Antarctica. The simulation successfully reproduced the characteristics of the observed GWs, such as the strength of vertical wind disturbances observed from the ground to 8 km altitude. The simulation showed ship‐wave‐like responses along the Antarctic coast, while, at higher altitudes, the wave pattern changed significantly due to the vertical structure of the background wind. Another interesting finding from the simulation is the presence of a wave pattern with a horizontal wavelength of approximately 25 km. The wavefronts of these waves align with the turbulent region formed downwind of a steep terrain along the coastline. The GWs are likely generated by the uplift of air along a particular type of atmospheric feature near the ground, which explain the upward transport of momentum observed by the radar. Key Points: Numerical simulations of gravity waves (GWs) over Syowa Station, Antarctic, successfully reproduce their amplitudes and momentum fluxesShip‐wave responses along the coastal terrain and wave filtering in the vertical structure of background winds are observedGWs are radiated from the lift of an airmass along an isentropic surface hump associated with a near‐surface a hydraulic jump [ABSTRACT FROM AUTHOR]

In this study, a modified form of the total mechanical energy budget equation is developed for 3-D turbulent flows with different hydraulic regimes in open-channel transitions, from which the effect of all turbulence parameters can be evaluated by applying some equalizations and RANS numerical simulations. The total energy equation is also used to extract an explicit relationship for energy loss based on turbulence parameters. The findings are presented in the form of the application of the relationship to calculate the energy loss based on simulation results for subcritical turbulent flow and hydraulic jump in open-channel transitions, which leads to identifying the effect of non-homogeneity and anisotropy of turbulence on flow energy balance. The results show that the work done by viscous shear stresses, the viscous diffusion of turbulence, and the turbulent diffusion have little to no effect on the total mechanical energy budget of open-channel turbulent flows; instead, the effect of the variations of turbulent kinetic energy and the work done by turbulence stresses is more significant. The benefit of using the modified energy equation is demonstrated by the potential for evaluating the details that were not previously considered. [ABSTRACT FROM AUTHOR]

Internal waves drive ocean mixing and enhance the transport of heat, momentum and other tracers in shelf seas. We collected observations of mixing over a 30‐day period from three cross‐shore moorings placed on the 330, 200 and 150 m isobaths on the offshore side of a pelagic ridge on the Australian North West Shelf. The region is forced by energetic surface and internal tides, exhibits non‐linear internal waves, experiences flow‐topography interactions, and is subject to episodic intense wind events. This complex forcing drove energetic diapycnal mixing at all sites. We identified five dominant internal wave forcing categories: mode‐1 waves at low‐frequency (time scales from double the buoyancy period to 4 hr), mode‐1 waves at high‐frequency (HF) (time scales between the buoyancy period and double the buoyancy period), mode‐2 waves, internal bores, and internal hydraulic jumps. Overall, just 15% of mixing events accounted for 90% of the total observed heat flux over the record. Mixing during internal wave events accounted for as much as 50% of the total heat flux in some locations. Of the internal wave categories, HF mode‐1 waves were the most significant contributors to the total heat flux at all sites (∼20%). On the other hand, internal bores made significant contributions to mixing only at the 200 and 150 m moorings; they made no contribution to mixing at the 330 m mooring. At the shallowest mooring, the different internal wave categories all made similar contributions to the total flux, indicating an increasingly complicated relationship between the evolving internal wavefield and the mixing. Plain Language Summary: Internal waves propagate along the density gradients found beneath the ocean's surface layer, analogous to surface waves propagating along the sharp density gradient where air and water meet. These waves play an important role in the distribution of nutrients, heat, contaminants, and other tracers in the ocean, especially in coastal regions where the waves break. The density structure of the ocean, the tidal and wind forcing, and the seabed features result in many different types of internal waves, each of which travel and break differently. In this work, we examine the mixing caused by different types of internal waves as they travel up and over a subsurface ridge on the Australian North West Shelf. We found that most of the significant mixing resulted from relatively rare events, which often occurred during internal wave forcing events. The magnitude of mixing increased in shallower waters due to internal waves breaking and causing energetic turbulent flows. However, the wave types that were the most significant for mixing changed depending on the location on the shelf and the depth. High‐frequency internal waves were generally the most significant contributor to mixing. Internal bores, a class of waves moving upslope near the seabed, did dominate the total ocean mixing near‐bottom at some locations. Key Points: Energetic but short‐lived nonlinear internal wave events drove most of the vertical turbulent heat flux over the month‐long recordInternal wave events evolved over relatively short time scales and relatively short spatial scalesEnergetic internal wave events contribute significantly to mixing in shelf seas [ABSTRACT FROM AUTHOR]

Small-scale processes at the southwestern boundary of the Ulleung Basin (UB) in the Japan/East Sea (JES) were examined using combined ship-based and moored observations along with model output. Model results show baroclinic semidiurnal tides are generated at the shelf break and corresponding slope connecting the Korea/Tsushima Strait with the UB and propagate into the UB with large barotropic-to-baroclinic energy conversion over the slope. Observations show high-frequency internal wave packets and indicate strong velocity shear and energetic turbulence associated with baroclinic tides in the stratified bottom layer. Solitary-like waves with frequencies from 0.2N to 0.5N (buoyancy frequency N) were found at the edge of the shelf break with supercritical flow. For subcritical flow, a hydraulic jump formed over the shelf break with weakly dispersive internal lee waves with frequencies varying from 0.5N to N. These high-frequency lee waves were trapped in the stratified bottom layer, with wave stress similar to the turbulent stress near the bottom. The power loss due to turbulent bottom drag can be an important factor for energy loss associated with the hydraulic jump. Turbulent kinetic energy dissipation rates of ∼10−4 W kg−1 were found. Large downward heat and salt fluxes below the high-salinity core mix warm/salty Tsushima Current Water with cold/low-salinity JES Intermediate Water. Mixing over the shelf break could be very important to the JES circulation since the calculated diapycnal upwelling (1–6 m day−1) at the shelf break and slope is substantially greater than the basin-averaged estimate from chemical tracers and modeling studies. Significant Statement: The Japan/East Sea (JES) is a marginal sea, enclosed by Japan, Korea, and Russia. This study describes mixing processes over the shelf break connecting the northern Korea/Tsushima Strait (KTS) with the southern Ulleung Basin (UB), where the warm, high-salinity Kuroshio water carried by the Tsushima Current interacts with southward-flowing subsurface water masses in the JES. Our analysis suggests that the shelf break and slope between the KTS and the UB are vital areas for water-mass exchange in the southern JES. The enhanced mixing at the shelf break may impact water masses and circulation over the entire JES. [ABSTRACT FROM AUTHOR]

Turbulent diapycnal mixing is important for the estuarine circulation between basins of the Baltic Sea as well as for its local ecosystems, in particular with regard to eutrophication and anoxic conditions. While the interior of the basins is overall relatively calm, stratified flow over steep bathymetric features is known as a source of strong turbulent mixing. Yet, current in situ observations often cannot capture the spatio-temporal development of dynamic and intermittent turbulent mixing related to overflows over rough bathymetry. We present observational oceanographic data together with openly accessible high-resolution bathymetry from a prototypical sill and an adjacent deep channel in the sparsely sampled Southern Quark located in the Åland Sea, connecting the northern Baltic Proper with the Bothnian Sea. Our data were acquired during two 1-week cruises on R/V Electra in February–March 2019 and 2020. We collected high-resolution broadband acoustic observations of turbulent mixing together with in situ microstructure profiler measurements, and current velocities from acoustic Doppler current profilers. We found that a temporally reversing non-tidal stratified flow over the steep bathymetric sill created a dynamic and extremely energetic environment. The observed flow reversed during both cruises on timescales of a few days. Saltier, warmer, and less oxygenated deep water south of the sill was partly blocked, the reversing flow was at times hydraulically controlled with hydraulic jumps occurring on both sides of the sill, and high spatial variability occurred in the surface layer on small scales. Dissipation rates of turbulent kinetic energy, vertical turbulent diffusivities, and vertical salt flux rates were increased by 3–4 orders of magnitude in the entire water column in the vicinity of the sill compared to reference stations not directly influenced by the overflow with average dissipation rates near the sill between 10 -7 and 10 -6 W kg -1 , average vertical diffusivities of 0.001 m 2 s -1 in the halocline and up to 0.1 m 2 s -1 below the halocline, and average vertical salt flux rates around 0.01 g m -2 s -1 in the halocline and between 0.1 and 1 g m -2 s -1 below the halocline. We suggest, based on acoustic observations and in situ measurements, that the underlying mechanism for the highly increased mixing across the halocline is a combination of shear and topographic lee waves breaking at the halocline interface. We anticipate that the resulting deep- and surface-water modification in the Southern Quark directly impacts exchange processes between the Bothnian Sea and the northern Baltic Proper and that the observed mixing is likely important for oxygen and nutrient conditions in the Bothnian Sea. [ABSTRACT FROM AUTHOR]

Hydraulic jump is used for dissipation of kinetic energy downstream of hydraulic structures such as spillways, chutes, and gates. In the present study, the experimental measurements and numerical simulation of the free hydraulic jump by applying Flow-3D software in six different conditions of adverse slope, roughness, and positive step were compared. It should be noted that two turbulence models including k-ε and RNG were used for numerical simulation. Based on the results, simulation accuracy using the RNG model was more than the k-ε model. The statistical indices of NRMSE, ME, NS, and R² for comparing the water surface profile were obtained at 34.3, 0.0052, 0.995, and 983 for the application of the RNG model, respectively. Also, using the RNG model, the values of these indices for the velocity profile were obtained at 14.92, 0.127, 0.9982, and 962, respectively. In general, the error of the simulated water surface and velocity profile were obtained at 5.31 and 12.4 percent, respectively. Moreover, the maximum error of the numerical simulation results of D2/D1, Lj/D2, and Lr/D1 was ±12, ±12, and 16%, respectively. Therefore, the use of Flow-3D software with the application of the RNG turbulence model is recommended for numerical simulation of the hydraulic jump in different situations. [ABSTRACT FROM AUTHOR]

Turbulence and pressure fluctuations are key elements in the bed protection design of hydraulic structures. However, their roles in a hydraulic jump are not yet fully understood, and the nature of their relationships are not conclusive. In order to better understand the relationships between pressure fluctuations and flow characteristics of a hydraulic jump downstream of a weir, detailed measurements of flow kinematics using the nonintrusive techniques of particle image velocimetry and bubble image velocimetry and pressure using voltage-type pressure gauges were carried out in this study. The physical modeling of the hydraulic jump was carried out using the simultaneous measurements of pressure and turbulent flow properties. The distributions of flow properties, such as water level and velocity, were assessed in each case. Based on the measurements, the correlations between the pressure fluctuations and the variables were investigated by coupling the statistical values of the variables at the same points. The analysis results show that the water level and turbulence intensity are the main factors influencing the pressure fluctuations in the hydraulic jump. Using these factors, an empirical formula and dimensionless numbers are proposed to show that the pressure fluctuations depend on the bubble flow behavior. [ABSTRACT FROM AUTHOR]

The hydraulic jump is a rapid transition state from supercritical to subcritical flow that occurs commonly in rivers, prismatic channels, and downstream of spillways. In this study, the characteristics of the hydraulic jump in a stilling basin downstream of the spillway chute channel with the slopes of α = 12° and 30° were investigated experimentally for different Froude numbers of incoming flow, Fr1 = 7, 7.5, 8, 9, 10, and 12, and relative heights of sill in the range of 4 < hs/h1 (S) < 13 (hs, the sill height, h1 the flow depth at toe of the jump, S relative height). The velocity field was measured by laser Doppler Anemometry in the experiments, it was particularly focused on the effects of both different structural configurations and flow conditions on the hydraulic jump and energy dissipation ratio. Experimental measurements showed that the length of the hydraulic jump and the roller zone increases with the decrease of the sill height for α = 12° and 30°. In addition, the length of the hydraulic jump and roller zone increased with decreasing Froude numbers. The turbulence intensity in the jump region was determined to be greater than the turbulence intensity in the region near the bottom of the stilling basin. The turbulence intensity, in general, tended to decrease with decreasing Froude number. [ABSTRACT FROM AUTHOR]

The kilometer-long sub-surface mooring 'KmT', densely instrumented with 760 high-resolution temperature 'T-'sensors, demonstrates details of turbulent mixing in the vicinity of a large seamount. Away from the internal wave breaking zone above the seafloor, turbulence is observed in two cases. It is found in thin layers along isopycnals providing non-smooth dispersal, as well as induced by internal wave breaking following strongly non-linear interaction as in a hydraulic jump more than 500 m above the local seafloor. Turbulence levels for these cases are relatively low and high, respectively, but always one to two orders of magnitude larger than in the ocean interior far from topography. Both cases imply the importance of underwater topography like a seamount for deep-sea turbulence. The seamount functions as a lens focusing internal waves into a turbulence-generator. [ABSTRACT FROM AUTHOR]

Turbulent diapycnal mixing is important for the estuarine circulation between basins of the Baltic Sea as well as for its local ecosystems, in particular with regard to eutrophication and anoxic conditions. While the interior of the basins is overall relatively calm, stratified flow over steep bathymetric features is known as a source for strong turbulent mixing. Yet, current in situ observations often cannot capture dynamic and intermittent turbulent mixing related to overflow over rough bathymetry. We present observational oceanographic data together with openly accessible high-resolution bathymetry from a prototypical sill and an adjacent deep channel in the sparsely-sampled Southern Quark located in the Åland Sea, connecting the Northern Baltic Proper with the Bothnian Sea. Our data include high resolution broadband acoustic observations of turbulent mixing, in situ microstructure profiler measurements, and current velocities from Acoustic Doppler Current Profilers and were acquired during two one-week cruises in February–March 2019 and 202. A temporally reversing non-tidal stratified flow over the steep bathymetric sill created a dynamic and extremely energetic environment. Saltier, warmer, and less oxygenated deep water south of the sill was partly blocked, the reversing flow was at times hydraulically controlled with hydraulic jumps occurring on both sides of the sill, and sub-mesoscale processes in the surface layer leading to high spatial variability at small scales. Mixing and vertical salt flux rates were increased by 3–4 orders of magnitude in the entire water column in the vicinity of the sill compared to reference stations not directly influenced by the overflow. We suggest based on acoustic observations and in situ measurements that underlying mechanisms for the highly increased mixing across the halocline are a combination of shear and topographic lee waves which are breaking at the halocline interface. We anticipate that the resulting deep- and surface-water modification in the Southern Quark directly impacts exchange processes between the Bothnian Sea and the Northern Baltic Proper and that the observed mixing is likely important for oxygen and nutrient conditions in the Bothnian Sea. Our results contribute to the knowledge on turbulent mixing processes in the Åland Sea and can help to improve mixing parametrizations in numerical models of the area. [ABSTRACT FROM AUTHOR]

This paper focuses on air–water interactions during pipe filling. The air–water mixed flow is related to a mobile hydraulic jump in the horizontal pipe section. The trapped water–air front at the crown of the pipe bridge determines the upstream boundary conditions for the stratified flow, suppressed hydraulic jump, and slug flow regions in the horizontal pipe section. The velocity field, the water level, and the pressure were measured at different stages of the transitional flow process. A full-scale two-phase computational fluid dynamics model, with two-equation eddy viscosity turbulence to account for small scales of motion, was used to predict the air pocket dynamics. The paper suggests that in the case of a frozen upstream water–air front, the formation of a hydraulic jump downstream can be explained by long-wave-type instability, which is confirmed by the free-surface supercritical flow Froude number condition. The hydraulic jump that merges stratified flow and slug flow is characterized by the speed of the surge wave, which is determined by the pressure, cross-sectional area of water flow, and density changes. A mixing efficiency parameter was introduced to explain the dissipation of turbulent energy due to the air–water mixing front of the suppressed hydraulic jump. [ABSTRACT FROM AUTHOR]

In the last two decades, the hydraulic jump has been extensively studied. In this article, attempt is made to have a comprehensive look at different characteristics of this complicated phenomenon. The aim of the present work is classification, comparison, and analysis of many research works on hydraulic jumps during the past years. It was found that there was no significant difference between jump characteristics such as the sequent depth and surface profile with developed or undeveloped approach flow, but air–water characteristics such as void fraction and bubble count rate are significantly affected. The present study also discusses the research results on pressure fluctuations, velocity field, turbulence characteristics, and air–water properties in a hydraulic jump. Investigating previous studies shows that most of the relationships presented for different characteristics of the hydraulic jump such as velocity or air concentration are dependent on other variables which are not available without measurements. The length of the stilling basin is considered equal to the length of the jump. Various definitions are given for the jump length. The results show that using the decay rate of pressure fluctuation, the stilling basin length could be calculated by less than 5% difference compared to the defined USBR I standard stilling basin length. [ABSTRACT FROM AUTHOR]

Air–water mixing associated with high turbulence is a common hydraulic phenomenon, where the transport of entrained air bubbles and the dissipation of turbulent energy are key processes affecting the air–water mass transfer. Herein hydraulic jumps were selected as a seminal case of self-air-entrainment in transitional water flow, and the air–water flow properties were investigated at high Froude numbers from 10.5 to 13.5. The analysis of air concentration distributions and bubble size spectra enabled deviation of the rates of bubble diffusion and turbulence dissipation. The study was facilitated with re-analyses of earlier experimental data for smaller Froude numbers between 3.8 and 10. The spatial evolution of the diffusion and dissipation rates suggested that the diffusion of air bubbles and dissipation of turbulent structures were not independent processes, and, at high Froude numbers, the mix of air and water was subject to re-aeration of the turbulent shear layer by the roller. [ABSTRACT FROM AUTHOR]

Scour downstream of smooth and rough rigid aprons under wall jets has been studied experimentally. Effect of apron roughness on scour has been investigated, and quantification of reduction in the scour depth due to rough apron has been performed. Characteristics of velocity and turbulence over smooth and rough aprons as well as within the scour hole have been analyzed to study the behavior of the jet and its interaction with the rough apron. Results show that there is a significant reduction in the equilibrium scour depth due to roughness. A maximum of 82.8% and a minimum of 31.1% reduction in the equilibrium scour depth was observed due to inducing roughness over the rigid apron. Velocity characteristics establish the cause of reduction in the equilibrium scour depth, which is due to reduction in the erosive capacity of the jet as it moves over the rough apron. The potential core of the jet gets consumed at a much lesser length due to roughness over the apron than over a smooth apron, as the boundary layer develops at a smaller distance. Further, it was observed that it takes a smaller length for the flow to get fully developed under the rough apron as compared with the smooth apron. Based on the results of the present analysis, recommendation can be made for use of roughness over the apron to restrict scour due to wall jets. [ABSTRACT FROM AUTHOR]

Near-critical turbulent axisymmetric free-surface flow over a horizontal bottom is investigated. Assuming that undular hydraulic jumps occur at large radii, an asymptotic analysis of the governing equations is performed in the double limit of very large Reynolds numbers and Froude numbers close to the critical value 1. The results are kept free of turbulence modelling due to a specific coupling of the two limiting processes. The final result of the asymptotic analysis is a new steady-state version of an extended Korteweg–de Vries (KdV) equation for the free-surface elevation. The extended KdV equation is derived as a uniformly valid differential equation, describing the flow near the origin of the undular jump as well as far downstream. Numerical solutions of the extended KdV equation show that circular undular jumps can develop if the reference state is located in the region where the effect due to axisymmetry prevails over the effect of friction. In this case, the solution oscillates over a very long distance until the accumulating friction effects force a breakdown. The comparison between the theories of undular jumps in turbulent and inviscid flows shows that friction is of minor importance near the development of the undular jump. However, friction has to be taken into account to describe the flow further downstream. Remarkably, the extended KdV equation is valid and yields undular solutions for both turbulent source and sink flow. [ABSTRACT FROM AUTHOR]

Measuring flow depths in free-surface turbulent flows can be challenging due to their fast dynamics and the presence of aeration. This study analyses the suitability of a low-cost sensor, the Intel® RealSense™ D435 RGB-D camera, for characterization of a highly aerated case study: the hydraulic jump. As with all instrumentation, special care must be taken to ensure accurate measurements. In this case, two different methods to calibrate depth estimations (accounting for set-up and any instrument precision) are presented, both leading to similar results. The main advantage of the presented instrumentation is its capability to measure 3D surfaces with high temporal and spatial resolution. Results are presented primarily in 2D in order to evaluate the flow depth estimation quality of this new technique with 2D data available in literature. The employed sensor showed a similar level of uncertainty as previous, well-established instrumentation for the study of free-surface elevations, amplitudes and frequencies of turbulent fluctuations. [ABSTRACT FROM AUTHOR]

In this study, a depth-averaged numerical model was employed to investigate the two-dimensional flow features of transitional open-channel flows from a supercritical to a subcritical state. Compared to a shallow-water model, the proposed model incorporates supplementary terms to account for the effects of non-uniform velocity and non-hydrostatic pressure distributions. The model equation was solved numerically by means of the Adams–Bashforth–Moulton scheme. A wide variety of transitional open-channel flow problems such as hydraulic jumps was considered for assessing the suitability of the numerical model. The results of the model for the free-surface profile, pressure distribution, and characteristics of the first wave of an undular jump were compared with the experimental data, and the agreement was found to be satisfactory. Despite the effects of the three-dimensional characteristics of the flow and the bulking of the flow caused by air entrainment, the model performed reasonably well with respect to the simulations of the mean flow characteristics of the curvilinear turbulent flow problems. Furthermore, the results of this investigation confirmed that the model is more suitable for analyzing near-critical turbulent flow problems without cross-channel shock waves. [ABSTRACT FROM AUTHOR]

A hydraulic jump is a sudden transition from a supercritical to subcritical flow with a broad range of turbulence Scales. The fluctuating nature of the flow such as oscillations of jump toe position and production of large eddies are visible in pseudo-periodic manners. Energy dissipation of hydraulic jump occurs with Low-frequency large scale pressure fluctuations which can cause damage and erosion and endanger the security of the structures. In the present study, the effects of discontinuous roughness elements of lozenge shape on the fluctuations of pressure in hydraulic jump have been investigated.

Steady turbulent near‐critical free‐surface flow over a slightly inclined bottom with an oblique roughness discontinuity is considered. An asymptotic analysis for Froude numbers close to the critical value 1 and large Reynolds numbers results in an extended Korteweg–de Vries (KdV) equation describing the free‐surface elevation without the need of turbulence modeling. Two new integral relations can be derived from the extended KdV equation. For enlarged downstream bottom roughness, a new type of undular jump solutions with fully developed flow both upstream and downstream exists. Numerical solutions of the extended KdV equation show that an increasing downstream bottom roughness enhances the development of undulations. [ABSTRACT FROM AUTHOR]

An along-channel momentum budget is quantified in the near-field plume region of a controlled river flow entering Doubtful Sound, New Zealand. Observations include highly resolved density, velocity and turbulence, enabling a momentum budget to be constructed over a control volume. Estimates of internal stress (τ) were made from direct measurements of turbulence dissipation rates (ϵ) using vertical microstructure profiles. High flow speeds of the surface plume over 2 m s -1 and strong stratification (N2∼10-1 s -2) resulted in enhanced turbulence dissipation rates (ϵ>10-3 W kg -1) and internal stress (τ>10-2 m 2 s -2) at the base of the surface layer. Internal waves were observed propagating along the base of the plume, potentially released subsequent to a hydraulic jump in the initial 1 km downstream of the plume discharge point. The momentum flux divergence of these internal waves suggests that almost 15 % of the total plume momentum can be transported out of the system by wave radiation, therefore playing a crucial role in the redistribution of momentum within the near-field plume. Observations illustrate that the evolution of the momentum budget components vary between the distinct surface plume layer and the turbulent, shear-stratified interfacial layer. Within the surface plume, a momentum balance was achieved. The dynamical balance demonstrates that the deceleration of the plume, driven by along-channel advection, is controlled by turbulence stress from the plume discharge point to as far as 3 km downstream. In the interfacial layer, however, the momentum equation was dominated by the turbulence stress term and the balance was not closed. The redistribution of momentum within the shear-stratified layer by internal wave radiation and other hydraulic features could account for the discrepancy in the budget. [ABSTRACT FROM AUTHOR]

This study considers a two-layer fluid with constant density in each layer connected by a layer of continuously varying density for flows past topography in which hydraulic jumps with lee vortices are expected based on shallow-water theory. Numerical integrations of the Navier–Stokes equations at a Reynolds number high enough for a direct numerical simulation of turbulent flow allow an examination of the internal mechanics of the turbulent leeside hydraulic jump and how this mechanics is related to lee vortices. Analysis of the statistically steady state shows that the original source of lee-vortex vertical vorticity is through the leeside descent of baroclinically produced spanwise vorticity associated with the hydraulic jump. This spanwise vorticity is tilted to the vertical at the spanwise extremities of the leeside hydraulic jump. Turbulent energy dissipation in flow through the hydraulic jump allows this leeside vertical vorticity to diffuse and extend downstream. The present simulations also suggest a geometrical interpretation of lee-vortex potential-vorticity creation, a concept central to interpretations of lee vortices based on the shallow-water equations. [ABSTRACT FROM AUTHOR]

An along-channel momentum budget is quantified in the near-field plume region of a controlled river flow entering Doubtful Sound, New Zealand. Observations include highly resolved density, velocity and turbulence, enabling a momentum budget to be constructed over a control volume. Estimates of internal stress (τ) were made from direct measurements of turbulence dissipation rates (ε) using vertical microstructure profiles. High flow speeds of the surface plume over 2 m s-1 and strong stratification (N² ~ 10-1 s-2) resulted in enhanced turbulence dissipation rates (ε > 10-3 W kg-1) and internal stress (τ > 10-2 m² s-2) at the base of surface layer. An observed transition from a supercritical to sub-critical flow regime in the initial 1 km indicates the presence of an internal hydraulic jump and the subsequent release of internal gravity waves. The momentum flux divergence of these internal waves suggests that almost 15% of the total plume momentum can be transported out of the system by wave radiation, therefore playing a crucial role in the redistribution of momentum within the near-field plume. Observations illustrate that the evolution of the momentum budget components vary between the distinct surface plume layer and the turbulent, shear-stratified interfacial layer. Within the surface plume, a momentum balance was achieved. The dynamical balance demonstrates that the deceleration of the plume, driven by along-channel advection, is controlled by turbulence stress from the plume discharge point to as far as 3 km downstream. In the interfacial layer however, the momentum equation was dominated by the turbulence stress term and the balance was not closed. The redistribution of momentum within the shear-stratified layer by the observed hydraulic jump and internal wave radiation could account for the discrepancy in the budget. [ABSTRACT FROM AUTHOR]

In the present work, oscillating characteristics and cyclic mechanisms in hydraulic jumps are investigated and reproduced using a weakly-compressible XSPH scheme which includes both an algebraic mixing-length model and a two-equation turbulence model to represent turbulent stresses. The numerical model is applied to analyze oscillations of different hydraulic jump types based on the laboratory experiments. The comparison between SPH and experimental results shows an influence of different turbulence models on the amplitude spectrum and peak amplitude of the time-dependent surface elevation upstream and downstream of the hydraulic jump. By analyzing a single cycle of the oscillating phenomena of a hydraulic jump it is possible to indicate their correlation with the vortex structures of the roller. Furthermore, analysis of the oscillating phenomena indicates a correlation among the surface profile elevations, velocity components and pressure fluctuations. This observation leads to conclude that oscillations phenomena are particularly important for analysis of the turbulence characteristics. [ABSTRACT FROM AUTHOR]

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier-Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k-ε model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon. [ABSTRACT FROM AUTHOR]

Hydraulic jumps are characterized by strong flow turbulence, flow aeration, and three-dimensional flow motions. Whereas comprehensive research into hydraulic jumps on smooth bed has improved the understanding of flow aeration and turbulence, limited research has been done of hydraulic jumps on rough beds. Herein novel experiments were conducted in hydraulic jumps on uniformly-distributed bed macroroughness. Both air-water flow patterns and basic air-water flow properties were investigated. The hydraulic jumps on the rough bed exhibited some remarkable differences compared with smooth bed jumps including some preaeration of the flow upstream of the jump, an upwards shift of the jump roller and a clear water-flow region underneath the jump. Air-water flow measurements were conducted with a phase-detection probe, showing similar distributions of air-water flow properties for the rough and smooth bed jumps. Comparative analyses highlighted some distinctive effects of the bed roughness including an upwards shift of the hydraulic jump and an increase in bubble count rate and void fractions in the region close to the jump toe. In the second half of the hydraulic jumps, the rough bed led to a clear-water region with large-scale vortices which were advected downstream. The present study highlighted the potential that improved and nonstandard invert designs may have for flow manipulations and design enhancements. [ABSTRACT FROM AUTHOR]

The study presents experimental investigations of spatial turbulence intensity and scales of turbulent eddies (macroeddies) in a rectangular channel and the impact of the hydraulic jump on their vertical and streamwise distributions over a flat and scoured bed. The results of four tests and two different discharge rates are presented. Intensive mixing caused by the hydraulic jump has an impact on the instantaneous velocity, turbulence intensity and sizes of macroeddies, as well as their vertical and longitudinal distributions along the channel. The largest differences in turbulence characteristics were reported directly after the hydraulic jump, above the eroded bed. The interaction between the stream of the increased turbulence and the bed is a direct cause of formation of scour downstream water structures, which has a great effect on overall flow characteristics. The scour hole that arose downstream the jump moderated, in a small degree, the turbulence intensity at its end. Just next to the hydraulic jump only the small longitudinal relative sizes of macroeddies were present, while at the end of the analyzed reach, downstream of the scour, the relative scale reached around 1.5 depth of the stream. [ABSTRACT FROM AUTHOR]

The modelling of complex free surface flows over weirs and in the vicinity of bridge piers is presented in a numerical model emulating open channel flow based on the Reynolds Averaged Navier-Stokes (RANS) equations. The importance of handling the turbulence at the free surface in the case of different flow regimes using an immiscible two-phase RANS Computational Fluid Dynamics (CFD) model is demonstrated. The free surface restricts the length scales of turbulence and this is generally not accounted for in standard two-equation turbulence modelling approaches. With the two-phase flow approach, large-velocity gradients across the free surface due to the large difference in the density of the fluids can lead to over-production of turbulence. In this paper, turbulence at the free surface is restricted with an additional boundary condition for the turbulent dissipation. The resulting difference in the free surface features and the consequences for the solution of the flow problem is discussed for different flow conditions. The numerical results for the free surface and stream-wise velocity gradients are compared to experimental data to show that turbulence damping at the free surface provides a better representation of the flow features in all the flow regimes and especially in cases with rapidly varying flow conditions.

A hydraulic jump is the rapid transition from a supercritical to subcritical flow. This transition is characterized by large-scale turbulence and energy dissipation. Despite the importance of understanding the hydraulic jump to design hydraulic structures, few studies have aimed on hydraulic jumps in U-shaped channels. In this paper, the 3D pattern of hydraulic jumps in U-shaped channels is studied numerically. The variations of the flow free surface are predicted using the volume of fluid scheme. Also, the flow field turbulence is simulated using the standard $$k-\varepsilon $$ and RNG $$k-\varepsilon $$ turbulence models. According to the numerical modeling results, the standard $$k-\varepsilon $$ turbulence model estimates the flow characteristics with more accuracy. A comparison between the laboratory and numerical results shows that the numerical model simulates the flow field characteristics with good accuracy. For example, in the hydraulic jump model with a relative discharge $$({q=Q/{\sqrt{( {gD^{5}})}}})$$ equal to 0.321 and a Froude number $$({{F}_1})$$ equal to 4.85, the values of MAPE, RMSE and $${R}^{2}$$ are calculated 7.617, 0.022 and 0.989, respectively. Next, 45 numerical models are simulated in different hydraulic conditions and some relationships are provided for calculating the sequent depth $$({{h_2 }/{h_1 }})$$ , hydraulic length $$({{L_\mathrm{j}}/{h_1}})$$ and roller length $$({{L_\mathrm{r} }/{h_1}})$$ ratios by analyzing their results. [ABSTRACT FROM AUTHOR]

The characteristics of three-dimensional vortical flow structures in submerged hydraulic jumps (generated downstream of a sluice gate) are analyzed in this paper. Results of a careful experimental investigation of the mean flow as well as turbulence statistics obtained with the use of Acoustic Doppler Velocimetry (ADV) and Particle Tracking Velocimetry (PTV) are presented and discussed. Experiments encompass incident Froude numbers ( Fr 1 ) of 3, 4 and 5, and submergence factors ( S ) ranging from 0.18 to 1.04. First, distributions in three vertical planes of values of the stream-wise velocity component and turbulent kinetic energy ( TKE ) are shown. With this information, the influence of Fr 1 and S on turbulence statistics is assessed. For the first time to the best of our knowledge, an approximately self-similar behavior of the profiles of TKE in the fully-developed region of the submerged jump is reported herein. A “climb effect” in the TKE is identified, very much in agreement with what occurs with the velocities. Then, the analysis focuses on the zone located near the gate, aiming at explaining the physical mechanisms which are responsible for the vorticity of vertical axis in that area. A relationship between the length scale of the roller of horizontal axis ( L rsj ) and that of the vortices of vertical axis ( L v ) is introduced, revealing that the dynamics of the two vortices are strongly linked. Compelling evidence sustaining that vorticity of vertical axis appears as a consequence of boundary-layer separation associated with the lateral walls is also provided. Finally, the anisotropy of turbulence in the outskirts of the vertical vortices is addressed, finding that such anisotropy is a consequence rather a cause of the presence of the vortices. [ABSTRACT FROM AUTHOR]

This study describes a downslope wind storm event observed over the Medicine Bow range (Wyoming, USA) on 11 January 2013. The University of Wyoming King Air (UWKA) made four along-wind passes over a five-hour period over the mountain of interest. These passes were recognized as among the most turbulent ones encountered in many years by crew members. The MacCready turbulence meter aboard the UWKA measured moderate to severe turbulence conditions on each pass in the lee of the mountain range, with eddy dissipation rate values over 0.5 m2/3 s-1. Three rawinsondes were released from an upstream location at different times. This event is simulated using the non-hydrostatic Weather Research and Forecast (WRF) model at an inner-domain resolution of 1 km. The model produces a downslope wind storm, notwithstanding some discrepancies between model and rawinsonde data in terms of upstream atmospheric conditions. Airborne Wyoming Cloud Radar (WCR) vertical-plane Doppler velocity data from two beams, one pointing to the nadir and one pointing slant forward, are synthesized to obtain a two-dimensional velocity field in the vertical plane below flight level. This synthesis reveals the fine-scale details of an orographic wave breaking event, including strong, persistent downslope acceleration, a strong leeside updraft (up to 10 m·s-1) flanked by counter-rotating vortices, and deep turbulence, extending well above flight level. The analysis of WCR-derived cross-mountain flow in 19 winter storms over the same mountain reveals that cross-mountain flow acceleration and downslope wind formation are difficult to predict from upstream wind and stability profiles. [ABSTRACT FROM AUTHOR]

An analytical solution of nondimensional hydraulic energy equation is derived in cosine form for the flow in rectangular open channels considering nonhydrostatic pressure and nonuniform velocity distributions across flow depth and friction and turbulent losses. The new inverted energy equation is a single equation describing all the three roots of the nondimensional hydraulic energy equation. The energy losses due to turbulence and bed shear are also implicitly accounted. Only two roots out of the three roots are practically significant, which denote the two alternate depths and are distinguishable for subcritical and supercritical flow, respectively. These equations yield direct determination of alternate depths in a single step, avoiding an iterative procedure. The use of the new equations is illustrated through worked-out examples. The new single-term analytical inverted equations are computationally simple and useful for academicians, field engineers, and practitioners in directly solving in a single step the problems of energy-equation inversion often encountered when dealing with transitions in a channel section, and flows over a dam-spillway and under a sluice gate, with correction-factors and loss coefficients estimated or known. [ABSTRACT FROM AUTHOR]

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. • Complicated relationship was shown between the three-dimensional free-surface characteristics and varying Froude number. • Unique features of turbulent velocity redistribution were detailed at the first standing wave. • Transition from an undular jump to a breaking jump is a process of localization of flow disturbance with increasing Fr. [ABSTRACT FROM AUTHOR]