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Environmental Fluid Mechanics

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ISSN (Print) 1573-1510 - ISSN (Online) 1567-7419
Published by Springer-Verlag

[2180 journals] [SJR: 0.732] [H-I: 23]

The role of coherent turbulent structures in explaining scalar dissimilarity within the canopy sublayer
- Abstract: Abstract Scalar similarity is widely assumed in models and interpretation of micro-meteorological measurements. However, in the air space within and just above the canopy (the so-called canopy sublayer, CSL) scalar similarity is generally violated. The scalar dissimilarity has been mainly attributed to differences in the distribution of sources and sinks throughout the canopy. Since large-scale coherent structures in the CSL (e.g. double roller and sweep/ejection) arise from the instabilities generated by the interaction between the mean flow and the canopy, they may encode key dynamical features about the production term responsible for the source–sink dissimilarity of scalars. Therefore, it is reasonable to assume that the geometric attributes of coherent structures are tightly coupled to the onset and the vertical extent of scalar dissimilarity within the CSL. Large-eddy simulation (LES) runs were used to investigate the role of coherent structures in explaining scalar dissimilarity among three scalars (potential air temperature, water vapour and $\text{ CO }_2$ concentration) within the CSL under near-neutral conditions for horizontally uniform but vertically varying vegetation leaf area density. It was shown that coherent structures, when identified from the first mode of a novel proper orthogonal decomposition (POD) approach, were able to capture some features of the scalar dissimilarity in the original LES field. This skill was quantified by calculating scalar–scalar correlation coefficients and turbulent Schmidt numbers of the original field and the coherent structures, respectively. However, coherent structures tend to magnify the magnitude of scalar–scalar correlation, particularly in cases where this correlation is already strong. The ability of coherent structures to describe more complex features such as the scalar sweep-ejection cycle was also explored. It was shown that the first mode of the POD does not capture the relative importance of sweeps to ejections in the original LES field. However, the superposition of few secondary coherent structures, derived from higher order POD modes, largely diminish the discrepancies between the original field and the POD expansion.
  PubDate: 2013-12-01
Experimental and numerical study on the shear velocity distribution along one or two dunes in tandem
- Abstract: Abstract This paper investigates, experimentally and numerically, the shear velocity distribution along a single transverse dune and along two closely spaced dunes, analyzing the flow effects of one dune upon the other. The paper focuses on two-dimensional models simulating transverse sand dunes. The shape of the two pile geometries studied is described by sinusoidal curves, one having a maximum slope of $32^{\circ }$ and the other $27.6^{\circ }$ , with leeward flow separation. The tests were carried out for two undisturbed wind speeds and the experimental data obtained through wind-tunnel modeling encompass flow visualization and shear-velocity results. A generally good agreement is observed between the experimental measurements and computational results. From the inquiry between shear velocity distributions and published eroded contours for the same geometries, it appears the Bagnold’s approach is insufficient in the prediction of threshold conditions in wake flows formed in the dune’s leeward side.
  PubDate: 2013-12-01
Removing the boundary influence on negatively buoyant jets
- Abstract: Abstract A comprehensive laboratory study of negatively buoyant discharges is presented. Unlike previous studies, here the focus is on generating data sets where influences of the bottom boundary have been eliminated. There are significant discrepancies in the published dilution data for these flows and a contributing factor is the large variation in the bottom boundary condition. A Laser-induced Fluorescence system is employed to gather flow spread, peak concentration (minimum dilution) and trajectory data for a wide range of densimetric Froude numbers and initial discharge angles. Data from these experiments are compared with previously published data, along with predictions from integral models and a revised form of the previously published semi-analytical solutions. The new data sets are not distorted by mixing processes associated with the bottom boundary and therefore provide the basis for more meaningful assessments of the predictive capabilities of existing models, given that the influences of the bottom boundary on contaminant mixing are not incorporated into these models. In general the models assessed are able to predict key geometric quantities with reasonable accuracy, but their minimum dilution predictions are conservative. Importantly dilution at the return point shows a strong dependence on the initial discharge angle and this could have important implications for the design of discharge systems.
  PubDate: 2013-12-01
Hydrodynamic characteristics and related mass-transfer properties in open-channel flows with rectangular embayment zone
- Abstract: Abstract Consecutive groynes and embayments form dead water zones, where sedimentation and high concentrations of pollutants are often observed. It is thus very important to understand the mass and momentum exchange between the main channel and side cavities in rivers and hydraulic engineering structures. The spanwise gradient of the streamwise velocity near the junction produces small-scale turbulent vortices because of shear instability. Furthermore, large-scale horizontal circulation is also generated in the cavity zone. These coherent turbulent structures play a significant role in mass and sediment transfer at the boundary between the mainstream and embayment. However, the relation between turbulence and mass transfer is poorly understood. In this study, we performed particle image velocity and laser-induced fluorescence experiments using a laboratory flume, laser light sheets and a high-speed CMOS camera. We examined the exchange properties of a dye as a function of bed configuration and sedimentation effect. Both primary and secondary gyres were observed in the flat bed and downward-sloping bed, whereas the primary gyre was prevalent in the upward-sloping bed. Moreover, the horizontal circulation strongly affected the mass-transfer properties between the mainstream and side cavity.
  PubDate: 2013-12-01
Performance and validation of a coupled parallel ADCIRC–SWAN model for THANE cyclone in the Bay of Bengal
- Abstract: Abstract An accurate prediction of near-shore sea-state is imperative during extreme events such as cyclones required in an operational centre. The mutual interaction between physical processes such as tides, waves and currents determine the physical environment for any coastal region, and hence the need of a parallelized coupled wave and hydrodynamic model. The present study is an application of various state-of-art models such as WRF, WAM, SWAN and ADCIRC used to couple and simulate a severe cyclonic storm Thane that developed in the Bay of Bengal during December 2011. The coupled model (ADCIRC–SWAN) was run in a parallel mode on a flexible unstructured mesh. Thane had its landfall on 30 December, 2011 between Cuddalore and Pondicherry where in-situ observations were available to validate model performance. Comprehensive experiment on the impact of meteorological forcing parameters with two forecasted tracks derived from WRF model, and JTWC best track on the overall performance of coupled model was assessed. Further an extensive validation experiment was performed for significant wave heights and surface currents during Thane event. The significant wave heights measured along satellite tracks by three satellites viz; ENVISAT, JASON-1 and JASON-2, as well in-situ near-shore buoy observation off Pondicherry was used for comparison with model results. In addition, qualitative validation was performed for model computed currents with HF Radar Observation off Cuddalore during Thane event. The importance of WRF atmospheric model during cyclones and its robustness in the coupled model performance is highlighted. This study signifies the importance of coupled parallel ADCIRC–SWAN model for operational needs during extreme events in the North Indian Ocean.
  PubDate: 2013-12-01
Small-scale spatial variability of turbulence statistics, (co)spectra and turbulent kinetic energy measured over a regular array of cube roughness
- Abstract: Abstract The spatial variability of flow and turbulence properties above an outdoor scale model of regular cube roughness under neutral stability is investigated using eight simultaneously employed sonic anemometers which are characterized by an extra short transducer span (0.05 m) and high sampling rate (50 Hz). Measurements are conducted in a layer between the top of the cubes with a plan area density of 0.25 and two times the height of the roughness, $H$ . Large spatial variability (horizontal and vertical) is observed at the two lowest measurement levels ( $z=H$ and $1.25H$ ) for all variables considered which include mean wind, Reynolds stress, integral statistics, (co)spectra, budget of turbulent kinetic energy and a spatial quadrant analysis of the momentum transfer. The spatial inhomogeneity almost disappears at $z = 1.5H$ where normalized variables attain homogeneous surface layer values for neutral stratification. The present results support a new conceptual framework to explain the turbulence behavior just above the canopy consisting of two sublayers which develop in response to the strongly varying surface. Although an individual measurement location below $z = 1.5H$ is unable to produce representative turbulence statistics above the present bluff body roughness, averaging across a sufficient number of measurement locations to achieve complete spatial sampling of all surface characteristics (canyon spaces, rooftops, etc.), produces representative statistics even at heights which are probably still within the roughness sublayer with values close to the respective inertial subrange predictions.
  PubDate: 2013-11-23
Shallow wake behind exposed wood-induced bar in a gravel-bed river
- Abstract: Abstract Recent theoretical research indicates that dynamics of shallow flows can be strongly affected by waves developing on the free surface. In this study a shallow wake with an oblique pressure wave behind a model of a tree-centered emergent bar is investigated in a gravel-bed river. A bar was constructed in a shallow river reach with nearly uniform flow. The structure of flow was assessed with an array of velocimeters. Flow visualization with a solute of fluorescent dye complemented the measurements and provided qualitative information on the wake behavior. This study indicates that quantitative criteria for shallow wakes classification developed in laboratory setups are not straightforward in explaining the field results. According to the wake stability criteria, the expected dynamics for examined wake flow is a vortex street (VS) type. Contrary to this expectation, measurements and visualizations in this study show that mean momentum differential and turbulent vortices in the wake decrease stronger than expected in VS type and therefore the wake should be classified as unsteady bubble type with a weak downstream instability. Analysis of velocity differential dynamics in the examined shallow wake suggests that the bed friction alone is insufficient to explain the inconsistency of VS criterion whereas accounting for advective fluxes driven by inhomogeneous pressure field leads to a correct prediction of the wake behavior.
  PubDate: 2013-11-22
Turbulence suppression by suspended sediment within a geophysical flow
- Abstract: Abstract Experiments are performed in a mixing box to evaluate the effect of suspended sediment on turbulence generated by an oscillating grid. Quartz-density sand of varying sizes and concentrations is used, and particle image velocimetry is employed to quantify only the fluid phase. Results show that (1) while a relatively large secondary flow field is present in the box, turbulence is a maximum near the grid and it decreases systematically toward the water surface; (2) relatively high concentrations of fine sediment can markedly alter this secondary flow field and significantly decrease both the time-mean and turbulent kinetic energy within the flow, yet these same sediment concentrations have little effect on the integral time and length scales derived for each velocity component; and (3) the overall turbulence suppression observed can be related to the transfer of energy from the fluid to the sediment and the maintenance of a suspended sediment load rather than commonly employed turbulence modulation criteria. These experimental data demonstrate unequivocally that the presence of a suspended sediment load can significantly reduce overall turbulent kinetic energy, and these results should be applicable to a range of sediment-laden geophysical flows.
  PubDate: 2013-11-17
On the representation of urban heterogeneities in mesoscale models
- Abstract: Abstract The size and arrangement of the obstacles and the presence of a source of heat (anthropogenic heat flux) are distinctive characteristics of an urban area. These two elements, together with the specific applications oriented to improve citizen’s comfort, determine the way urban heterogeneities are represented in mesoscale models. In this contribution two examples are presented. In the first a microscale fluid dynamics model is used to investigate the role of organized motions (dispersive fluxes) of a passive tracer emitted at the surface in a staggered and in an aligned array of cubes. The impact of the dispersive flux, that can reach 90 % of the total flux in the staggered array, is then assessed in a column model. The second example deals with the representation of anthropogenic heat fluxes and the estimation of thermal comfort by means of an urban canopy parameterization with a simple building energy model, implemented in a mesoscale model. The simulation of a typical summer day over the city of Madrid (Spain) shows that the anthropogenic heat fluxes have the largest impact on the air temperature in the evening-night, and that the presence of the city prolongs to the late evening the period of thermal discomfort, compared with the rural areas surrounding the city. The paper is concluded by pointing out that future work must be devoted to deep on the relationship between the real morphology of a city and the simplified morphology adopted in the urban canopy parameterizations.
  PubDate: 2013-11-14
Sediment processes and flow reversal in the undular tidal bore of the Garonne River (France)
- Abstract: Abstract A tidal bore is a series of waves propagating upstream as the tidal flow turns to rising, and the bore front corresponds to the leading edge of the tidal wave in a funnel shaped estuarine zone with macro-tidal conditions. Some field observations were conducted in the tidal bore of the Garonne River on 7 June 2012 in the Arcins channel, a few weeks after a major flood. The tidal bore was a flat undular bore with a Froude number close to unity: $\hbox {Fr}_{1} = 1.02$ and 1.19 (morning and afternoon respectively). A key feature of the study was the simultaneous recording of the water elevation, instantaneous velocity components and suspended sediment concentration (SSC) estimates, together with a detailed characterisation of the sediment bed materials. The sediment was some silty material ( $\hbox {d}_{50} \approx 13~\upmu \hbox {m}$ ) which exhibited some non-Newtonion thixotropic behaviour. The velocity and SSC estimate were recorded simultaneously at high frequency, enabling a quantitative estimate of the suspended sediment flux at the end of the ebb tide and during the early flood tide. The net sediment flux per unit area was directed upstream after the bore, and its magnitude was much larger than that at end of ebb tide. The field observations highlighted a number of unusual features on the morning of 7 June 2012. These included (a) a slight rise in water elevation starting about 70 s prior to the front, (b) a delayed flow reversal about 50 s after the bore front, (c) some large fluctuations in suspended sediment concentration (SSC) about 100 s after the bore front and (d) a transient water elevation lowering about 10 min after the bore front passage. The measurements of water temperature and salinity showed nearly identical results before and after the tidal bore, with no evidence of saline and thermal front during the study.
  PubDate: 2013-11-07
Gravity currents with tailwaters in Boussinesq and non-Boussinesq systems: two-layer shallow-water dam-break solutions and Navier–Stokes simulations
- Abstract: Abstract We consider the dam-break initial stage of propagation of a gravity current of density $\rho _{c}$ released from a lock (reservoir) of height $h_0$ in a channel of height $H$ . The channel contains two-layer stratified fluid. One layer, called the “tailwater,” is of the same density as the current and is of thickness $h_T (< h_0)$ , and the other layer, called the “ambient,” is of different density $\rho _{a}$ . Both Boussinesq ( $\rho _{c}/\rho _{a}\approx 1$ ) and non-Boussinesq systems are investigated. By assuming a large Reynolds number, we can model the flow with the two-layer shallow-water approximation. Due to the presence of the tailwater, the “jump conditions” at the front of the current are different from the classical Benjamin formula, and in some circumstances (clarified in the paper) the interface of the current matches smoothly with the horizontal interface of the tailwater. Using the method of characteristics, analytical solutions are derived for various combinations of the governing parameters. To corroborate the results, two-dimensional direct numerical Navier–Stokes simulations are used, and comparisons for about 80 combinations of parameters in the Boussinesq and non-Boussinesq domains are performed. The agreement of speed and height of the current is very close. We conclude that the model yields self-contained and fairly accurate analytical solutions for the dam-break problem under consideration. The results provide reliable insights into the influence of the tailwater on the propagation of the gravity current, for both heavy-into-light and light-into-heavy motions. This is a significant extension of the classical gravity-current theory from the particular $h_T=0$ point to the $h_T > 0$ domain.
  PubDate: 2013-11-06
Computational fluid dynamics assessment of damaging wind loads on the One Indiana Square tower
- Abstract: Abstract In this paper, we simulated damaging wind loads on the One Indiana Square tower in Indianapolis due to the storm of April 2nd 2006. We followed recommended practice guidelines for this urban wind modeling. First, a test case, Aerodynamics of Commonwealth Advisory Aeronautical Council (CAARC) building were modeled and simulated to compare with a publicly available experiment and other computational studies. Based on the modeling parameters in the CAARC study, then, as a clean building configuration, we modeled the One Indiana tower alone without surrounding buildings. Finally, the flow field around the tower including nearby downtown buildings were simulated. We used the Fluent flow analysis software tools. The domain was meshed using unstructured grids, the first boundary layer grid element being 10 cm (4 in.) and 15 cm (6 in.) in height from the tower and the ground for the CAARC building and the One Indiana tower, respectively. Two different wind directions of 260 $^\circ $ and 280 $^\circ $ at 137 km/h (85 mph) speed were considered to estimate wind loads on the One Indiana tower façades. Simulated pressure distributions on the tower and flow patterns over the downtown buildings were discussed to draw conclusions about the mechanism of extreme wind load that caused the damage. The simulations revealed that suction forces are almost twice higher hence more damaging at the corners of the west façades than straight wind. It was also seen in the simulation results that upstream building topology, specifically Chase, One America, and some low-rise towers, augmented the actual wind load unfavorably on the One Indiana Square tower. Although this study presents a specific case, the applicability of its findings are of more general interest. Similar wind events are common especially during storm seasons both in urban and suburban areas. In similar incidents, one can follow the same procedure to analyze their problems as certain modeling guidelines were followed in this study.
  PubDate: 2013-11-02
Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope
- Abstract: Abstract The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, $(g_o^{\prime } Q)^{1/3}$ , which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.
  PubDate: 2013-10-30
Large eddy simulation of dispersion around an isolated cubic building: evaluation of localized dynamic $k_\mathrm{SGS}$ -equation sub-grid scale model
- Abstract: Abstract In the present study, the prediction accuracy of a dynamic one-equation sub-grid scale model for the large eddy simulation of dispersion around an isolated cubic building is investigated. For this purpose, the localized dynamic $k_\mathrm{SGS} $ -equation model (LDKM) is employed and the results are compared with the available experimental data and two other classic sub-grid scale models, namely, standard Smagorinsky–Lilly model (SSLM) and dynamic Smagorinsky–Lilly model (DSLM). It is shown that the three SGS models give results in good agreement with experiment. However, near the ground level of the leeward wall, dimensionless time-averaged concentration, $\langle K\rangle $ , profile is not quite similar to the experimental data. It is also demonstrated that the LDKM predicts the values of $\langle K\rangle $ on the roof, leeward and side walls more acceptably than the SSLM and DSLM. Whereas, the streamwise elongation of time-averaged structures of the plume shape is more over-estimated with the LDKM than with the other two SGS models. In terms of numerical difficulty, the LDKM is found to be stable and computationally reasonable. In addition, it does not suffer from a flow dependent constant such as the Smagorinsky coefficient employed in the SSLM model.
  PubDate: 2013-10-23
Dynamics of the head of gravity currents
- Abstract: Abstract The present work experimentally investigates the dynamics of unsteady gravity currents produced by lock-release of a saline mixture into a fresh water tank. Seven different experimental runs were performed by varying the density of the saline mixture in the lock and the bed roughness. Experiments were conducted in a Perspex flume, of horizontal bed and rectangular cross section, and recorded with a CCD camera. An image analysis technique was applied to visualize and characterize the current allowing thus the understanding of its general dynamics and, more specifically, of the current head dynamics. The temporal evolution of both head length and mass shows repeated stretching and breaking cycles: during the stretching phase, the head length and mass grow until reaching a limit, then the head becomes unstable and breaks. In the instants of break, the head aspect ratio shows a limit of 0.2 and the mass of the head is of the order of the initial mass in the lock. The average period of the herein called breaking events is seen to increase with bed roughness and the spatial periodicity of these events is seen to be approximately constant between runs. The rate of growth of the mass at the head is taken as a measure to assess entrainment and it is observed to occur at all stages of the current development. Entrainment rate at the head decreases in time suggesting this as a phenomenon ruled by local buoyancy and the similarity between runs shows independence from the initial reduced gravity and bed roughness.
  PubDate: 2013-10-10
Spatial evolution of coherent motions in finite-length vegetation patch flow
- Abstract: Abstract A number of experimental studies on submerged canopy flows have focused on fully-developed flow and turbulent characteristics. In many natural rivers, however, aquatic vegetation occurs in patches of finite length. In such vegetated flows, the shear layer is not formed at the upstream edge of the vegetation patch and coherent motions develop downstream. Therefore, more work is neededz to reveal the development process for large-scale coherent structures within vegetation patches. For this work, we considered the effect of a limited length vegetation patch. Turbulence measurements were intensively conducted in open-channel flows with submerged vegetation using Particle Image Velocimetry (PIV). To examine the transition from boundary-layer flow upstream of the vegetation patch to a mixing-layer-type flow within the patch, velocity profiles were measured at 33 positions in a longitudinal direction. A phenomenological model for the development process in the vegetation flow was developed. The model decomposed the entire flow region into four zones. The four zones are the following: (i) the smooth bed zone, (ii) the diverging flow zone, (iii) the developing zone and (iv) the fully-developed zone. The PIV data also confirmed the efficiency of the mixing-layer analogy and provided insight into the spatial evolution of coherent motions.
  PubDate: 2013-10-01
Two-phase modeling of sediment clouds
- Abstract: Abstract A sediment cloud release in stagnant ambient fluid occurs in many engineering applications. Examples include land reclamation and disposal of dredged materials. The detailed modeling of the distinct characteristics of both the solid and fluid phases of the sediment cloud is hitherto unavailable in the literature despite their importance in practice. In this paper, the two-phase mixing characteristics of the sediment cloud are investigated both experimentally and theoretically. Experiments were carried out to measure the transient depth penetration and the lateral spread of the sediment cloud and its entrained fluid using the laser induced fluorescence technique, with a range of particle sizes frequently encountered in the field (modeled at laboratory scale). A two-phase model of the sediment cloud that provides detailed predictions of the mixing characteristics of the individual phases is also proposed. The entrained fluid characteristics are solved by an integral model accounting for the buoyancy loss (due to particle separation) in each time step. The flow field induced by the sediment cloud is approximated by a Hill’s spherical vortex centered at the centroid and with the size of the entrained fluid. The particle equation of motion under the effect of the induced flow governs each computational particle. A random walk model using the hydrodynamic diffusion coefficient is used to account for the random fluctuation of particles in the dispersive regime. Overall, the model predictions of the two-phase mixing characteristics are in good agreement with the experimental data for a wide range of release conditions.
  PubDate: 2013-10-01
Passive scalar roughness lengths for atmospheric boundary layer flow over complex, fractal topographies
- Abstract: Abstract When modeling atmospheric boundary layer flow over rough landscapes, surface fluxes of flow quantities (momentum, temperature, etc.) can be described with equilibrium logarithmic law expressions, all of which require specification of a roughness length that is, physically, the elevation at which the flow quantity equals its surface value. In high Reynolds number flows, such as the atmospheric boundary layer, inertial forces associated with turbulent eddy motions are responsible for surface momentum fluxes (form, or pressure drag). Surface scalar fluxes, on the other hand, occur exclusively via diffusion in the immediate vicinity of the topography—the interfacial region—before being advected by turbulent eddy motions into the bulk of the flow. Owing to this difference in surface transfer mechanism, the passive scalar roughness length, $z_{0S}$ , is known to be less than the momentum roughness length, $z_0$ . In this work, classical relations are used to specify $z_{0S}$ during large-eddy simulation of atmospheric boundary layer flow over aerodynamically rough, synthetic, fractal topographies which exhibit power-law height energy spectrum, $E_h (k) \sim k^{\beta _s}$ , where $\beta _s$ is a (predefined) spectral exponent. These topographies are convenient since they resemble natural landscapes and $\beta _s$ can be varied to change the topography’s aerodynamic roughness (the study considers a suite of topographies with $-2.4 \le \beta _s \le -1.2$ , where $-2.4$ and $-1.2$ are the “most smooth” and “most rough” cases, respectively, corresponding with roughness Reynolds number, $Re_0 \approx 10$ and $300$ ). It is often assumed that $z_{0S}/z_{0} \approx 10^{-1}$ for all $Re_0$ . But results from this work show that the roughness length ratio, $z_{0S}/z_{0}$ , depends strongly on $Re_0$ , ranging between $10^{-3}$ and $10^{-1}$ .
  PubDate: 2013-10-01
Empirical equation for transverse dispersion coefficient based on theoretical background in river bends
- Abstract: Abstract There are different approaches to estimating the transverse dispersion coefficient in river mixing. Theoretical approaches have derived the dispersion coefficient from the concept of shear flow, which has dominant effects on the transverse mixing. Empirical approaches have developed an equation using the hydraulic and geometric data of rivers through dimensional analysis and regression techniques. These two equations interact closely with each other. For example, the complicated theoretical equation can be simplified by empirical approaches, and the functional relationships of the empirical equation can be derived from theoretical bases. In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the theoretical background in river bends. As a regression method, the least-square iterative method was used because the equation was a nonlinear model. The estimated dispersion coefficients derived by the new equation were compared with observed transverse dispersion coefficients acquired from natural rivers and coefficients calculated by the other existing empirical equations. From a comparison of the existing transverse dispersion equations and the proposed equation, it appears that the behavior of the existing formula in a relative sense is very much dependent on the flow condition and the river geometry. Moreover, the proposed equation does not vary widely according to variation of flow conditions. Also, it was revealed that the equation proposed in this study becomes an asymptotic curve as the curvature effect increases.
  PubDate: 2013-10-01
Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for embankments
- Abstract: Abstract The design floods of several reservoirs were recently re-evaluated and the revised spillway outflow could result in dam overtopping with catastrophic consequences for some embankment structures. Herein a physical study was performed on flat and pooled stepped spillways with a slope typical of embankments $(\uptheta = 26.6^{\circ })$ and four stepped configurations were tested: a stepped spillway with flat horizontal steps, a pooled stepped spillway, and two stepped spillways with in-line and staggered configurations of flat and pooled steps. The focus of the study was on the flow aeration, air–water flow properties, cavity flow processes, and energy dissipation performances. The results demonstrated the strong aeration of the flow for all configurations. On the in-line and staggered configurations of flat and pooled steps, the flow was highly three-dimensional. The residual head and energy dissipation rates at the stepped chute downstream end were calculated based upon the detailed air–water flow properties. The results showed that the residual energy was the lowest for the flat stepped weir. The data for the stepped spillway configuration with in-line and staggered configurations of flat and pooled steps showed large differences in terms of residual head in the transverse direction. Altogether the present results showed that, on a $26.6^{\circ }$ slope stepped chute, the designs with in-line and staggered configurations of flat and pooled steps did not provide any advantageous performances in terms of energy dissipation and flow aeration, but they were affected by three-dimensional patterns leading to some flow concentration.
  PubDate: 2013-10-01