Showing papers in "Journal of Hydraulic Research in 2011"
TL;DR: In this article, scale effects arise due to force ratios which are not identical between a model and its real-world prototype and result in deviations between the up-scaled model and prototype observations.
Abstract: Scale effects arise due to force ratios which are not identical between a model and its real-world prototype and result in deviations between the up-scaled model and prototype observations. This review article considers mechanical, Froude and Reynolds model–prototype similarities, describes scale effects for typical hydraulic flow phenomena and discusses how scale effects are avoided, compensated or corrected. Four approaches are addressed to obtain model–prototype similarity, to quantify scale effects and to define limiting criteria under which they can be neglected. These are inspectional analysis, dimensional analysis, calibration and scale series, which are applied to landslide generated impulse waves. Tables include both limiting criteria to avoid significant scale effects and typical scales of physical hydraulic engineering models for a wide variety of hydraulic flow phenomena. The article further shows why it is challenging to model sediment transport and distensible structures in a physical hydrau...
490 citations
TL;DR: In this paper, experiments in a large-scale facility have been performed, for the measurement of wave attenuation, transmission and energy dissipation over artificial Posidonia oceanica, the most abundant seagrass species in the Mediterranean, supporting a highly bio-diverse habitat and is crucial in protecting against coastal erosion.
Abstract: Posidonia oceanica, the most abundant seagrass species in the Mediterranean, supports a highly bio-diverse habitat and is crucial in protecting against coastal erosion. In this work, experiments in a large-scale facility have been performed, for the measurement of wave attenuation, transmission and energy dissipation over artificial Posidonia oceanica. The effects of submergence ratio corresponding to the seagrass height divided by water depth, and seagrass density as the number of stems per square metre on the above characteristics are investigated. Measurements of wave height at different locations along the vegetation meadow indicate the wave attenuation along the Posidonia oceanica for three different submergence ratios and two seagrass densities. Results are also analysed with regard to the wave-induced flow within the meadow, and the effects of the submergence ratio and the seagrass density on the mean flow characteristics, based on data of mean velocities taken at three locations within the seagrass.
114 citations
TL;DR: In this paper, the applicability of the transient-based frequency response function (FRF) method for detecting leaks in complex series pipelines was investigated and two simple numerical experimental cases consisting of 3-series and 10-series pipes, respectively.
Abstract: This research investigates the applicability of the transient-based frequency-response function (FRF) method for detecting leaks in complex series pipelines. The behaviour of transient waves in these pipelines with internal series junctions indicates that junction reflections modify the system resonant frequencies but have a small effect on the leak-induced information contained within the system frequency responses. The analogous method previously developed for single pipelines is extended to complex series pipe systems by using the analytical transfer matrix method herein and the extended method is validated by two simple numerical experimental cases consisting of 3-series pipes and 10-series pipes, respectively. The applied results indicate that the extended FRF method can be applied to detect single and multiple leaks in complex series pipelines as long as the location and size of the resonant peaks of system frequency responses are accurately determined.
113 citations
TL;DR: In this article, a two-dimensional finite volume Godunov-type model was proposed to solve the shallow-water flooding problem and a much simplified condition to maintain well-balanced solutions around a wet-dry front was proposed.
Abstract: Dam-break flows usually occur in domains with complex geometric and topographic features and involve abrupt flow patterns. A dam-break model must therefore be able to effectively handle different flow types including transcritical flows or hydraulic jumps, deal with complex domain topography, capture repeating wet–dry interface and represent high roughness values in the floodplain. Herein, all of these objectives are achieved by extending a recent one-dimensional finite volume Godunov-type model into two dimensions for solving the shallow-water equations. While doing so, a much simplified condition to maintain well-balanced solutions around a wet–dry front is proposed and a two-dimensional friction source term discretization is derived under a suitable stability condition in relation to practical simulations. The two-dimensional model is successfully validated against three analytical benchmark tests and then assessed for predicting realistic dam-break flood events.
96 citations
TL;DR: In this paper, a detailed experimental data of high-temporal and spatial resolution on the breach of homogeneous non-cohesive embankments due to overtopping was obtained.
Abstract: Laboratory experiments were conducted to obtain detailed experimental data of high temporal and spatial resolution on the breach of homogeneous non-cohesive embankments due to overtopping. These results supplement earlier data for this embankment type by providing information on the breach discharge, longitudinal and transversal breach profiles, erosion rates and pore-water pressures within the embankment. Based on detailed experimental results, two breach phases are classified. Shear and tension failure mechanisms were identified from the analysis of the obtained cross-sectional breach profiles. Furthermore, the temporal cross-sectional analysis of the used non-cohesive granular material shows a different behaviour regarding the lateral breach widening and the breach slope failure. The data analysis indicates that the apparent cohesion represented by the pore-water pressure influences the stability of the breach side slopes and hence the complete breach process. This finding is confirmed by a dimensional...
94 citations
TL;DR: In this paper, an ODE for velocity distribution in open channel flows is presented based on an analysis of the Reynolds-averaged Navier-Stokes equations and a log-wake modified eddy viscosity distribution.
Abstract: An ordinary differential equation (ODE) for velocity distribution in open channel flows is presented based on an analysis of the Reynolds-averaged Navier–Stokes equations and a log-wake modified eddy viscosity distribution. This proposed equation allows to predict the velocity-dip-phenomenon, i.e. the maximum velocity below the free surface. Two different degrees of approximations are presented, a semi-analytical solution of the proposed ODE, i.e. the full dip-modified-log-wake law (fDMLW-law) and a simple dip-modified-log-wake law (sDMLW-law). Velocity profiles of the two laws and the numerical solution of the ODE are compared with experimental data. This study shows that the dip correction is not efficient for a small Coles' parameter, accurate predictions require larger values. The sDMLW-law shows reasonable agreement and seems to be an interesting tool of intermediate accuracy. The fDMLW-law, with a parameter for dip-correction obtained from an estimation of dip positions, provides accurate velocity p...
90 citations
TL;DR: In this article, an experimental study carried out in a flume to a scale of 1/20 is presented to assess the wave height attenuation induced by submerged meadows of Posidonia oceanica.
Abstract: An experimental study carried out in a flume to a scale of 1/20 is presented to assess the wave height attenuation induced by submerged meadows of Posidonia oceanica. After examination of the appropriate scaling laws and selection of the model material, an extensive test programme included both regular and random waves. A semi-empirical formulation for estimating the wave height transformation along the meadow is obtained, based on energy conservation and considering that dissipation is only due to drag forces. The latter were linearized to obtain an exponential decay law. The formulation proposed depends on the drag coefficient and includes also an empirical parameter accounting for wave steepness. The model improves previous results and extends its applicability to random waves. The drag coefficient associated to the meadows is found to be better related to the Keulegan–Carpenter parameter than to the Reynolds number. Its value is given also for models proposed by others.
84 citations
TL;DR: In this paper, a video camera was used to record the trajectory of inclined turbulent round jets with negative buoyancy discharging in a calm homogeneous fluid, and six different discharge angles from 45° to 90° to the horizontal were studied.
Abstract: Experimental results on inclined turbulent round jets with negative buoyancy discharging in a calm homogeneous fluid are presented. Six different discharge angles from 45° to 90° to the horizontal are studied, and the jet evolution is recorded by means of a video camera. Results concern the main geometrical characteristics of the jet trajectory, i.e. the initial terminal height of rise reached by the jet at flow initiation, the final terminal height of rise observed at steady state, the horizontal distance from the source at which the terminal height is observed and the horizontal distance to the point where the jet returns at the source elevation. The densimetric Froude number at the source ranges between 7 and 60, whereas the Reynolds number is generally higher than 6000. Results are given in dimensionless form and confirm theoretical considerations obtained by dimensional analysis.
81 citations
TL;DR: In this paper, the authors present experimental test results performed on a 1:10 scale model of the Piano Key Weir and determine the flow features along the weir depending on the upstream head.
Abstract: The Piano Key Weir is a type of labyrinth weir using overhangs to reduce the footprint of the foundation. These are directly placed on a dam crest. Together with its high discharge capacity for low heads, this geometry makes these weirs interesting in dam rehabilitation. However, the Piano Key Weir is a new weir type, first designed in 2001 and built from 2006 by Electricite de France. Even though experimental studies confirmed its appealing discharge capacities, the flow upstream, over and downstream of this complex structure is still not well known. This research presents experimental test results performed on a 1:10 scale model. The experiments aim at determining the flow features along the weir depending on the upstream head. The flow conditions are characterized in terms of specific discharge, velocity, pressure, water level and streamlines along the weir.
81 citations
TL;DR: In this article, physical model investigations on a stepped spillway scaled 1:10 of varying step height, chute angle and discharge are conducted with the objective to analyse the development of these air-water flow properties in the non-uniform flow region.
Abstract: In hydraulic engineering, stepped spillways are effective structures in regard to both energy dissipation and re-aeration processes. It is well known that flow depths and flow velocities generally depend on the spillway geometry in terms of slope and step-induced macro-roughness height on the one hand and the discharge on the other hand. Moreover, these parameters affect the air entrainment process and hence, the amount and the size of entrained air bubbles which are directly linked to the specific air–water interface being of particular significance for oxygen transfer. In this study, physical model investigations on a stepped spillway scaled 1:10 of varying step height, chute angle and discharge are conducted with the objective to analyse the development of these air–water flow properties in the non-uniform flow region. Measurements of air–water mixture velocity and air concentration are carried out by the use of an intrusive double-tip conductivity probe. It is found that the step-induced macro-roughne...
77 citations
TL;DR: In this paper, a micro-scale conductivity probe was used to measure the mean concentration of round turbulent negatively buoyant jets discharging into a calm homogeneous fluid at three different angles.
Abstract: Experiments on concentration measurements in round turbulent negatively buoyant jets discharging into a calm homogeneous fluid at three different angles are presented. Detailed measurements using a micro-scale conductivity probe were carried out at the horizontal location of the terminal rise height, mostly along the vertical of the axial jet plane and in the transverse direction. The dimensionless vertical distribution of the mean concentration is found to be asymmetric, whereas the transverse distribution is approximately Gaussian. At the same horizontal location, the vertical distribution of the concentration turbulent intensity has a maximum at a point systematically higher than the jet axis. The width of the mean concentration distribution, the heights to the location of the maximum mean concentration and to the maximum turbulent intensity as well as the minimum dilution are determined. From measurements in the region where the jet returns to the source elevation, the minimum dilution and the horizon...
Abstract: Vehicles parking in urban areas can often cause various hazards to people and buildings when they are swept away by flash floods. Therefore, it is necessary to investigate the appropriate criteria of vehicle stability in floodwaters. Different forces acting on partially submerged vehicles have been analysed, with a mechanics-based formula of incipient velocity being derived. Experiments were conducted to obtain the conditions of water depth and corresponding velocity at the threshold of vehicle instability for three typical types of die-cast model vehicles. The data were used to determine two key parameters. Incipient velocities for partially submerged prototype vehicles in floodwaters were estimated using two different approaches, including the predictions using the scale ratios and computations based on the formula. These critical conditions using the scale ratios compare well with the calculations using the derived formula, and the derived formula was also validated by the visually-observed data of swe...
TL;DR: In this article, the authors present experiments of dam-break flow on mobile bed in an abruptly expanding channel, the wider section being twice as wide as the narrow one, where sediment deposition occurred in the wider channel reach.
Abstract: This research presents experiments of dam-break flow on mobile bed in an abruptly expanding channel, the wider section being twice as wide as the narrow. The bed material consisted of coarse uniform sand. The flow near the one-sided flume expansion induces a two-dimensional morphological evolution. Important scour at the corner of the abrupt expansion was observed, while sediment deposition occurred in the wider channel reach. Measurements of the flow evolution and the final bed topography were obtained using ultrasonic sensors and digital imaging techniques, both having the advantage of being non-intrusive. The available experimental data consist of temporal water level evolutions at nine gauging points, water front propagations, velocity fields at given times at the free surface and topographical surveys of the final bed elevation at various cross-sections. This data set is available upon request to the scientific community for the validation of numerical models.
TL;DR: In this article, a new entropy-based approach for deriving a 2D velocity distribution in open-channel flow was developed, and the values determined using the proposed distribution were found to be in good agreement with the experimentally-measured velocity values.
Abstract: In this paper, considering time-averaged velocity as a random variable, two-dimensional (2D) velocity distributions in open-channel flow have been derived based on the Shannon entropy concept and the principle of maximum entropy. The velocity distributions so derived have limited practical use, since they contain too many parameters that need to be experimentally calibrated and hence are not convenient to apply. This work develops a new entropy-based approach for deriving a 2D velocity distribution in open-channel flow, thereby investigating a rectangular geometric domain. The derived distribution is parsimonious, and the values determined using the proposed distribution are found to be in good agreement with the experimentally-measured velocity values.
TL;DR: In this paper, a trapezoidal embankment was overtopped by three distinct types of waves: wave groups of compact form, wave groups embedded in a background wave field and a solitary wave.
Abstract: Prediction of individual wave overtopping events is important in assessing danger to life and property, but data are sparse and hydrodynamic understanding is lacking. Laboratory-scale waves of three distinct types were generated at the Coastal Research Facility to model extreme waves overtopping a trapezoidal embankment. These comprised wave groups of compact form, wave groups embedded in a background wave field, and a solitary wave. The inshore wave propagation was measured and the time variation of overtopping rate estimated. The total volume overtopped was measured directly. The experiments provide well-defined data without uncertainty due to the effect of reflection on the incident wave train. The dependence of overtopping on a range of wave shapes is thus determined and the influence of wave–wave interactions on overtopping assessed. It was found that extreme overtopping may arise from focused waves with deep troughs rather than large crests. Furthermore, overtopping waves can be generated from small...
TL;DR: In this article, the effects of flow acceleration on sand transport were investigated in an oscillating water tunnel to study the effect of acceleration skewness on sediment transport in the nearshore zone.
Abstract: New experiments under sheet flow conditions were conducted in an oscillating water tunnel to study the effects of flow acceleration on sand transport. The simulated hydrodynamic conditions considered flow patterns that drive cross-shore sediment transport in the nearshore zone: the wave nonlinearities associated with velocity and acceleration skewness and a negative mean current, the undertow. Net transport rates were evaluated from the sediment balance equation and show that (1) the acceleration skewness in an oscillatory flow produces a net sediment transport in the direction of the highest acceleration; (2) the net transport in the presence of an opposing current is negative, against the direction of the highest acceleration, and reduces with an increase in flow acceleration; and (3) velocity skewness increases the values of the net onshore transport rates.
TL;DR: In this paper, the effect of vegetation patches on the flow and turbulence characteristics of submerged vegetation patches has been studied, and two turbulence models were used to simulate patch presence and the results indicate that the patch length and the vegetation density dominate the turbulent development.
Abstract: The effect of a vegetation patch (VP) on the flow and turbulence characteristics is studied. Two turbulence models are used to simulate patch presence. Numerical results for both mean and turbulence flow characteristics are compared with available measurements to assess the performance of these models for dense and sparse submerged VPs. The mechanisms which control the turbulent development inside the VP are also discussed, and the patch effect on the downstream flow and turbulence is assessed. The results indicate that the patch length and the vegetation density dominate the turbulent development. An increase in the vegetation density causes acceleration of the development of flow velocity and turbulence characteristics inside the patch and increases the channel length downstream of the patch where its effect is significant. Also areas with increased and decreased values of bed shear stresses are observed at the initial part and at the end of the patch, respectively.
TL;DR: In this paper, a hybrid finite volume-finite difference numerical scheme is proposed to solve a set of two-dimensional extended Boussinesq equations where both nonlinear and dispersive effects are relevant and nonlinear shallow water equations where nonlinearity prevails over dispersion.
Abstract: A Boussinesq-type model is applied herein to study wave propagation and wave breaking over complex bathymetries reproducing common coastal features, namely plane and barred beaches, submerged bars and rip channels. A hybrid finite volume–finite difference numerical scheme solves a set of, in the horizontal plane, two-dimensional extended Boussinesq equations where both nonlinear and dispersive effects are relevant and nonlinear shallow water equations where nonlinearity prevails over dispersion. The shock-capturing features of the finite volume method enable an intrinsic representation of spilling wave breaking and runup. Comparisons with experimental data indicate that the numerical model adequately simulates wave transformation over submerged bars, correctly capturing wave breaking onset and termination including the related energy dissipation. The development of breaking-induced currents and their interaction with wave propagation are also well represented within the applicability range of the governin...
TL;DR: In this paper, the turbulent flow structures around an isolated spur dike located at three different approach flow angles are investigated, and it is found that the size and orientation of the horseshoe vortex system change considerably with the approach flow angle.
Abstract: The turbulent flow structures around an isolated spur dike located at three different approach flow angles are investigated. Detached eddy simulation is used at a channel Reynolds number of 45,000. Experimental velocity measurements were also conducted using acoustic Doppler velocimetry for validating the simulations. It is found that the size and orientation of the horseshoe vortex system change considerably with the approach flow angle. The main necklace vortex is largest in size and most coherent for 90°. Within this orientation it has larger amplitude bimodal oscillations compared to the 60° and 120° cases. A new scour mechanism is defined for the 60° case which is expected to generate more scour upstream of the spur dike. The possible scour area around the spur dike is found to be the maximum in the 90° case which is roughly by 15% larger than that of the 120° case.
TL;DR: Duan et al. as discussed by the authors gave an important contribution in the field of Hydraulic Research by proposing a new approach based on the concept of hydraulic flow and showed that the approach can be used to solve the problem of hydraulic power control.
Abstract: By H.-F. DUAN, M. GHIDAOUI, P.J. LEE, and Y.-K. TUNG, Journal of Hydraulic Research Vol. 48, No. 3 (2010), pp. 354–362 In the discussers' opinion, this paper gives an important contribution in the ...
TL;DR: In this article, a wide range of combinations of these two non-dimensional geometric parameters were tested at constant hydraulic conditions and five different types of flow patterns were identified, depending on the values of the length-to-width ratio and expansion ratio of the reservoir.
Abstract: Velocity fields in rectangular shallow reservoirs with different length-to-width and expansion ratios were investigated in an experimental study, to evaluate the effect of geometry on the flow field. A wide range of combinations of these two non-dimensional geometric parameters were tested at constant hydraulic conditions. Ultrasound velocity profilers were used to measure the horizontal velocity components across the entire reservoir surface, allowing for the visualization of streamlines and of the instantaneous and average velocities. Five different types of flow patterns were identified, depending on the values of the length-to-width ratio and expansion ratio of the reservoir. Asymmetrical flow patterns were found to develop for certain combinations of these geometric parameters despite the perfect reservoir symmetry. A critical comparison of these new experimental results with those of other works is provided.
TL;DR: In this article, a rigid-plug elastic-water model is developed by applying elastic water hammer to the majority of the water columns while applying rigid-water analysis to a small portion near the air-water interface.
Abstract: Pressure transients in a rapidly-filling pipe with an entrapped air pocket are investigated analytically. A rigid-plug elastic-water model is developed by applying elastic-water hammer to the majority of the water columns while applying rigid-water analysis to a small portion near the air–water interface. The proposed model is validated by the full elastic-water model and experimental data. It effectively avoids the interpolation error of the method of characteristics reducing its complexity when tracking the air–water interface. Moreover, the current model has the same accuracy as the full elastic-water model.
TL;DR: In this article, the motion of sediment particles over a transitionally rough bed is studied experimentally using a real-time high-speed imaging system using acoustic Doppler velocimetry.
Abstract: The motion of sediment particles over a transitionally-rough bed is studied experimentally using a real-time high-speed imaging system. Vertical distributions of the instantaneous flow velocities were measured using acoustic Doppler velocimetry. The sediment saltation trajectories and the associated velocity components were deciphered from the high-speed images using digital image processing techniques. Sediments of different sizes and specific weights were used for experimentation. Particles moving in both the rolling and the saltation regimes were tested. Stochastic deviations of the particle velocity, the particle acceleration and the angle of velocity vector orientation during its motion due to particle interactions with flow and the channel bed are quantified. The angle distributions and the acceleration fluctuations are approximately bell-shaped. Using the experimental data, a generalized single relation for particle velocity is proposed for saltation and rolling sediments. The results of particle m...
TL;DR: The results of an experimental study on the flow characteristics around a groin structure of various geometries and permeabilities are presented in this paper, where the velocity fields were observed using large-scale particle image velocimetry, whereas the maximum velocities were measured using an acoustic Doppler velocimeter.
Abstract: The results of an experimental study on the flow characteristics around a groin structure of various geometries and permeabilities are presented. The impermeable rectangular, the permeable pile, and the triangular-shaped groins are considered. The velocity fields were observed using large-scale particle image velocimetry, whereas the maximum velocities were measured using an acoustic Doppler velocimeter. An increased velocity at the groin tip and a broad range of the recirculation zones were observed for the impermeable rectangular groin. For the permeable pile groin, the velocity at the groin tip, the vortex strength, and the scale of the recirculation zone tended to decrease as the openings between the piles increased. Also, the triangular-shaped groin formed narrower and longer recirculation zones compared with the permeable pile groin of identical cross-sectional flow area. These quantitative findings on the flow patterns for groins of various geometries and permeabilities are practically important to...
TL;DR: In this article, a stochastic particle-particle collision model was designed to determine the collision probability along a particle trajectory, based on the assumption that interparticle collisions frequency may be described by the formula of kinetic gas theory.
Abstract: The effect of particle–particle collision on the trajectories of saltating grains in open-channel flows is investigated. The vertical distributions of saltating particles are also analysed. A stochastic particle–particle collision model was designed to determine the collision probability along a particle trajectory, based on the assumption that inter-particle collision frequency may be described by the formula of kinetic gas theory. This parameter is the key quantity for the calculation of collision probability. The Monte Carlo simulation method is used to obtain the velocity and concentration of saltating particles. It is the first attempt to apply a probabilistic inter-particle collision approach to Lagrangian modelling of saltating grains. Trajectories of different particles with and without particle–particle collision are compared with available data. The proposed procedure allows verification of the hypothesis regarding the effect of the particle–particle collision on sediment transport. The describe...
TL;DR: In this paper, an integrated numerical sediment transport model capable of solving both uniform and non-uniform transport equations while calculating grain size distributions is presented, coupled with external hydrodynamic codes which provide flow field and bed shear stress patterns.
Abstract: The development and validation of an integrated numerical sediment transport model capable of solving both uniform and non-uniform transport equations while calculating grain size distributions is presented. The model is coupled with external hydrodynamic codes which provide flow field and bed shear stress patterns. Transport equations are solved for an unlimited number of sediment size fractions. Two validation experiments involving unsteady flow in a channel bend and steady flow in a flume with lateral contraction were considered. Good agreement with measured bed deformations was found for non-uniform calculations with an exchange layer, whereas both uniform and non-uniform computations without the exchange layer resulted in comparably larger differences. In the channel bend experiment, the presence of an exchange layer was essential for achieving accurate modelling results, while its role was less pronounced in the lateral contraction experiment. Moreover, the sorting coefficient of the bed material wa...
TL;DR: In this paper, the characteristics of dividing critical flows in a 90° open-channel junction formed by three horizontal equal width branches are presented, conducted for various inflow discharges and downstream boundary conditions.
Abstract: An experimental study of the characteristics of dividing critical flows in a 90° open-channel junction formed by three horizontal equal-width branches is presented, conducted for various inflow discharges and downstream boundary conditions. Outflow discharges and flow depths were also measured. Four main flow patterns are identified considering the location and length of the hydraulic jumps that develop across the main and lateral channels. A relationship between the discharge division ratio and the tailwater Froude number is found, reproducing well the experimental data. Practical applications of this relationship include the design of open channel and pipe networks and one-dimensional numerical modelling of flood propagation in urban areas. The study shows also that a two-dimensional depth-averaged numerical model hardly gives better predictions of the discharge ratios because of the presence of three-dimensional features at the junction.
TL;DR: In this paper, the authors verify a numerical sediment transport model based on field data from a reach of the Austrian Danube River, to identify the influence of non-uniform bed-load transport modelling and the selected bed schematization on the simulation results and investigate the cause and the numerical reproducibility of spatio-temporal variations found in field data.
Abstract: The objectives of this research are to verify a numerical sediment transport model based on field data from a reach of the Austrian Danube River, to identify the influence of non-uniform bed-load transport modelling and the selected bed schematization on the simulation results and to investigate the cause and the numerical reproducibility of spatio-temporal variations found in field data. Simulation results based on variants of the transport equation by Meyer-Peter and Muller were compared to basket sampler and radio tracer stone observations. The best agreement was obtained for a non-uniform formulation with an exchange layer, while the uniform formulation of the transport equation underestimated the transport rates for discharges lower than the mean flow since it predicts a later onset of bed-load transport. The consideration of an exchange layer in the numerical code led to the prediction of bed-load sheets due to sorting waves, allowing the model to account for the spatio-temporal variability of field...
TL;DR: In this article, a simple and low-cost alternative for the quantitative characterization of quasi-two-dimensional shallow coherent structures is presented, based on the image pre-processing of flow visualizations and post-processing by means of the proper orthogonal decomposition.
Abstract: The identification of the spatial characteristics and the shedding frequencies of coherent structures in shallow flows usually involves the use of sophisticated equipment for velocity measurements such as laser Doppler anemometry or particle image velocimetry. In this work, a simple and low-cost alternative for the quantitative characterization of quasi two-dimensional shallow coherent structures is presented. The technique is based on the image pre-processing of flow visualizations and post-processing by means of the proper orthogonal decomposition. As an illustration of the method, the analysis of a shallow flow in the wake of a cylinder with a vortex-street pattern is presented. The method is able to discriminate concentration patches attached to the vortices and their advection, providing frequencies in excellent agreement with a previous study.
TL;DR: In this paper, a series approximation for the transitional motion at zero initial velocity was proposed by applying a nonlinear perturbation method and Rubey's universal drag law to the Boussinesq-Basset-Oseen equation.
Abstract: Motion of spheres falling through fluids is a classic problem in fluid mechanics. The problem is solved for steady motion and other special cases such as for small and large Reynolds numbers, but not yet for transitional flow motion because of the complicated drag law. Recently, a series approximation for the transitional motion at zero initial velocity was proposed by applying a nonlinear perturbation method and Rubey's universal drag law to the Boussinesq–Basset–Oseen equation. This research presents a simple closed-form solution to the problem for arbitrary Reynolds numbers at nonzero initial velocity. The proposed solution is confirmed with experimental literature data and reproduces all well-known asymptotic values. The results can be directly used for particle size analysis in hydraulics laboratories; they may also help understanding the fluid–particle interactions in environmental engineering, meteorology, and powder technology.