Bed Friction Research Articles

Peak discharge increase in hyperconcentrated floods

The peak of river floods usually decreases in the downstream direction unless it is compensated by freshwater inflow from tributaries. In the Yellow River (China) the opposite is regularly observed, where the peak discharge of river floods increases in the downstream direction (at a rate far exceeding the contribution from tributaries). This flood peak discharge increase is probably related to rapid morphological changes, to a modified bed friction, or to a combination of both. Yet the relative role of these processes is still poorly understood. This paper aims to analyze the relative contribution of bed erosion and friction change to the peak discharge increase, based on available data and a recently developed numerical model. Using this high-resolution, fully coupled morphodynamic model of non-capacity sediment transport, two hyperconcentrated floods characterized by downstream peak discharge increase are numerically reproduced and analyzed in detail. The results reveal that although erosion effects may contribute to the downstream discharge increase (especially in case of extreme erosion), for most cases the increase must be mainly due to a reduction in bed friction during peak discharge conditions. Additionally, based on the concept of channel storage reduction, the effects of decreasing bed friction and (very strong) bed erosion can be integrated in explaining the peak discharge increase.

Wave Transformation along Southwest Coast of India Using MIKE 21

Nearshore wave transformation is a complex coastal process of shoaling, refraction, diffraction, reflection, and energy dissipation due to bed friction and breaking contributing variations in the wave height, period and direction. A well defined sediment cell of about 45 km extending from Kovalam headland to Varkala cliff which forms a part of Thiruvananthapuram coast along the southwest coast of India, is selected for the wave transformation studies. In the present study MIKE 21 Spectral Wave model (DHI, 2011) was used. The model simulates the growth, decay and transformation of wind generated waves and swells both in offshore and coastal areas. Providing MIKE 21 SW with a suitable bathymetry is essential for obtaining reliable results from the model. Usually the offshore bathymetry is derived from C-MAP, ETOPO, GEBCO etc. and the nearshore bathymetry is generated from close grid bathymetric surveys. In this study offshore bathymetry was generated from GEBCO-08 grid which is a freely available software with 30 arc (∼ 1 km) resolution. In the nearshore zone, surveyed close grid bathymetric data were used. The other inputs such as wave measurements and wind data provided in the model were from observations in Lakshadweep Sea. Model result is calibrated with field observations along this sector. The model has efficiently simulated the process of shoaling and refraction along the coast. The percentage of observed shoaling is 12.7% at a distance of 24 km from the shoreline at a depth of 70m and it was seen to be increasing to 27.9% when it reached around 2.4 km from the shore at a depth of 10m. The model result also shows that the wave is almost aligned parallel to the coast as wave approaches the coast. This model result can be used for further applications in designing along this coast.

An evaluation of the Rouse theory for sand transport in the Oka estuary, Spain

The Rouse profile has been traditionally used to represent the vertical distribution of suspended sand in a marine benthic boundary layer. Yet it is one of the biggest unknowns in estuarine morphodynamics, largely due to uncertainties of the ratio of the sediment fall velocity to bed friction on which the Rouse exponent (R=ws/βku⁎) is based. A field campaign was carried out at three different locations in the Oka estuary, northern Spain, in order to examine these uncertainties. Each location differed in grain size and flow condition thus offering a wide range of settings. The first survey was inside the estuary (wave sheltered, flood tide dominated and relatively broad estuary section), the second was at the distal ebb delta (ebb tide dominated and narrow estuary section), and the third was over the wave exposed proximal ebb delta (wave/flood tidal current combined flows and open sea). The aim of this study is to evaluate the applicability of the Rouse (1937) theory for the distribution of sand in suspension throughout a turbulent benthic boundary layer. A modified version of a Helley–Smith sampler was used to trap sand and measure the vertical distribution of sand in the water column. As well, a 1200 ADCP was used to measure flow velocity and backscatter together with an ADV (turbulence). The sand traps were found to have a sampling efficiency of 44%. The grain size at all stations was finer near the surface and coarser near the bed. The sand transport inside the estuary (Station 1) is inwards dominant. By contrast, the sand concentration during the ebb tide was ten times higher than during the flood tide at Station 2 and even higher at Station 3, which suggests that the sand transport over the ebb delta is seawards. The average Rouse parameters for Stations 1, 2, and 3 are 0.48±0.035, 0.78±0.23, and 0.46±0.06 respectively, which correspond to a coefficient of proportionality of the movability number, (χ) of 4 (Van Rijn, 1993). These differ from previous findings of Villatoro et al. (2010) and Amos et al. (2010b).

Using an extreme bony prominence anatomical model to examine the influence of bed sheet materials and bed making methods on the distribution of pressure on the support surface

Bed sheets generate high surface tension across the support surface and increase pressure to the body through a process known as the hammock effect. Using an anatomical model and a loading device characterized by extreme bony prominences, the present study compared pressure distributions on support surfaces across different bed making methods and bed sheet materials to determine the factors that influence pressure distribution.The model was placed on a pressure mapping system (CONFORMat®; NITTA Corp., Osaka, Japan), and interface pressure was measured. Bed sheet elasticity and friction between the support surface and the bed sheets were also measured.For maximum interface pressure, the relative values of the following methods were higher than those of the control method, which did not use any bed sheets: cotton sheets with hospital corners (1.28, p = 0.02), polyester with no corners (1.29, p = 0.01), cotton with no corners (1.31, p = 0.003), and fitted polyester sheets (1.35, p = 0.002). Stepwise multiple regression analysis indicated that maximum interface pressure was negatively correlated with bed sheet elasticity (R2 = 0.74). A statistically significant negative correlation was observed between maximum interface pressure and immersion depth, which was measured using the loading device (r = −0.40 and p = 0.04).We found that several combinations of bed making methods and bed sheet materials induced maximum interface pressures greater than those observed for the control method. Bed sheet materials influenced maximum interface pressure, and bed sheet elasticity was particularly important in reducing maximum interface pressure.

Calibrating discharge, bed friction, and datum bias in hydraulic models using water level and surface current observations

[1] We show that observations of water surface elevation, surface velocity, and bathymetry can be used to calibrate multiple reach-scale parameters such as the discharge, the overall bed friction, and a water surface datum bias in a hydraulic model (FaSTMECH) for the depth-averaged flow in the braided reach of the Kootenai River near Bonners Ferry, ID. Remotely sensed surface velocity data acquired during a 2010 field experiment are converted to depth-averaged velocity using a uniform ratio of 0.79 computed from concurrent in situ observation of vertical profiles of velocity. The in situ measured discharge of the Kootenai River was approximately 220 m3/s. For given discharge forcing and downstream boundary condition provided by the measured water surface elevation, the FaSTMECH model was used to predict the horizontal variation of the depth-averaged velocity and the water surface elevation over the braided reach. The calibration considered here consists of varying the discharge, the bed friction coefficient and the water surface datum offset to find the combination that minimizes error metrics based on the streamwise profiles of the measured water level and maximum depth-averaged velocity. Composite error metrics that combine water level and velocity measurements are found to be more sensitive with respect to variation of the datum bias and the bed friction. We find that a composite error based on the total head is minimized for a discharge of 220 m3/s, friction coefficient of 0.005, and a datum offset of 40 cm.

Comparison Between Boussinesq and Shallow-Water Models in Predicting Solitary Wave Runup on Plane Beaches

The nonlinear shallow water equations and Boussinesq equations have been widely used for analyzing the solitary wave runup phenomenon. In order to quantitatively assess the merits and limitations of these two approaches, a shock-capturing scheme has been applied to numerically solve both sets of equations for predicting the runup processes over plane beaches. The analytical and experimental data available in the literature have been used as references in the assessment. In this study, the uniform sloping beach is preceded by a length of flat seafloor. When incident solitary waves are specified close to the slope, the two approaches are found to produce almost identical results for nonbreaking waves. For breaking waves, the Boussinesq equations give a better representation of the wave evolution prior to the breaking point, whereas they overestimate the short undulations accompanying the breaking process. If incoming solitary waves need to travel a long distance over a flat bed before reaching the slope, the shallow water equations cannot capture the correct waveform transformation, and the predicted runup depends heavily on the length of the flat-bed section. As this length approaches zero, however, the shallow water equations somehow give roughly the same maximum runup heights as those predicted by the Boussinesq model. The bed friction has little effect on the runup for small waves, but becomes important for large waves. The roughness coefficient needs to be calibrated to reproduce the measured runup heights of breaking waves.

TEKNİK NOTAkım Gözlem İstasyonlarında Yatak Sürtünme Katsayısı ve Eğiminin Sayısal Yöntemle Bulunması

Determination of Bed Friction Coefficient and Bottom Slope At Flow Gauging Stations Using A Numerical Method In this study, measured flow data obtained from natural streams is utilized to predict hydraulic characteristics and to validate conformity of the measured data sets. Section factor is computed from cross-section measurements. Relations between section factor and water depth are derived from synthetically enriched data based on measurements at high water levels. Bed friction and bed slope are determined by fitting logarithmic law to measured point velocity data. Thus, it’s shown that it can be possible to obtain more technical information from the traditional flow measurement data

Shallow wake behind exposed wood-induced bar in a gravel-bed river

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.

Experimental study of the water depth and rainfall intensity effects on the bed roughness coefficient used in distributed urban drainage models

Summary The work presented in this paper analyses the effect of water depth and rainfall intensity on the surface roughness coefficients used in overland flow models based on the shallow water equations. The relation between the Manning coefficient and the water depth and rainfall intensity has been quantified using different methodologies based on the analysis of two sets of experimental data. In the first set uniform overland flow conditions were generated, and the bed roughness coefficient was computed from direct measurements of the water depth and discharge. In the second set of experiments, unsteady rainfall–runoff transformations with different rainfall intensities were generated in a flume and computed with a shallow water model in which different bed friction formulations were implemented and calibrated. Results show that for very low water depth values there is a significant increase in the surface resistance, which is not captured by any standard bed friction formulation. Rainfall intensity also increases surface resistance especially as the water depth diminishes below a critical threshold. Using a Reynolds dependent formulation for the Manning coefficient improves model predictions.

Linear Stability Analysis of Open-Channel Shear Flow Generated by Vegetation

A linear stability analysis of flow in an open-channel partially covered with vegetation was performed. The differential drag between vegetated zones and adjacent nonvegetated zones is known to induce a lateral gradient of the streamwise velocity. The velocity gradient may result in flow instability in the shear layer around the edge of the vegetated zone causing the generation of discrete horizontal vortices. We assume that the base state flow field before the occurrence of instability is characterized by turbulencewith a smaller length scale than the flow depth, which is mainly generated by the bottom friction. By introducing perturbations to the flow depth as well as the stream- wise and transverse velocities in the base state, the conditions required for perturbations to grow in time were studied over a wide range of (1) Froude number, (2) normalized nonvegetated zone width, and three other dimensionless parameters that represent the relative effect of (3) bed friction, (4) vegetation drag, and (5) subdepth eddy viscosity. All parameters were found to have positive and negative growth rates of perturbations within their respective evaluated ranges. The characteristic vortex shedding frequencies associated with the maximum growth rate was compared with those observed in experiments. Although the analysis that employs a base state set without the large scale lateral motions was shown to be capable of predicting the order of magnitude of the frequencies, there is a systematic discrepancy between the predicted and observed frequencies, which may be due to the limitation of linear stability analysis. DOI: 10.1061/(ASCE)HY.1943-7900 .0000822. © 2014 American Society of Civil Engineers.

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.

LE of shallow mixing interfaces: A review

Eddy-resolving techniques have become a powerful tool to investigate shallow flows at both laboratory and field scale. In this paper several examples are given where high-resolution 3D numerical simulation are used to investigate the spatial development of mixing interfaces (MIs) forming in shallow environments like open channels with idealized and natural bathymetry where the bed friction plays a major role in the spatial development of the MI and associated large-scale turbulence. The focus is on the coherent structures forming within the MI and in its vicinity that control the momentum and mass exchange and heat transfer between the two sides of the MI. Examples include: (1) a MI developing in a flat-bed open channel downstream of a splitter wall separating two parallel fully-turbulent streams of different velocities, (2) a MI developing in a flat-bed open channel downstream of a 60\(^{\circ }\) wedge separating two non-parallel fully turbulent streams of different velocities, (3) a MI developing downstream of a river confluence for cases with a large and, respectively, a small difference between the mean velocities of the two streams. Stratification effects due to unequal densities of the two incoming streams are also discussed, (4) a MI developing between a main rectangular straight channel and a series of shallow embayments present at one of the channel banks. Besides using available experimental data to demonstrate that eddy resolving techniques can accurately predict the structure of the MI and its development, the paper discusses new insights into the physics of these flows obtained based on the simulations. The paper also provides an overview of the main numerical approaches that can be used to simulate the unsteady dynamics of the large scale turbulence in flows containing shallow MIs.

A novel approach to flow estimation in tidal rivers

Reliable estimation of river discharge to the ocean from large tidal rivers is vital for water resources management and climate analyses. Due to the difficulties inherent in measuring tidal‐river discharge, flow records are often limited in length and/or quality and tidal records often predate discharge records. Tidal theory indicates that tides and river discharge interact through quadratic bed friction, which diminishes and distorts the tidal wave as discharge increases. We use this phenomenon to develop a method of estimating river discharge for time periods with tidal data but no flow record. Employing sequential 32 day harmonic analyses of tidal properties, we calibrate San Francisco (SF), CA tide data to the Sacramento River delta outflow index from 1930 to 1990, and use the resulting relationship to hindcast river flow from 1858 to 1929. The M2 admittance (a ratio of the observed M2 tidal constituent to its astronomical forcing) best reproduces high flows, while low‐flow periods are better represented by amplitude ratios based on higher harmonics (e.g., ). Results show that the annual inflow to SF Bay is now 30% less than before 1900 and confirm that the flood of January 1862 was the largest since 1858.

Flow Structure around Bridge Piers of Varying Geometrical Complexity

Piers with back-to-back stems or columns and piers for which part of the foundation becomes exposed as a result of the development of scour over large periods of time or because of severe flood events are fairly common at bridge waterways. The present paper uses eddy-resolving numerical simulations to study flow and turbulence structure at piers of complex shape and/or with multiple components. In particular, the study considers cases with one and two back-to-back pier columns for which the section of the main column is neither circular nor rectangular. In addition to a design case for which the foundation of each pier column is submerged, the study analyzes a case when scour exposes part of the foundation of the main column. The results show that the shape and size of the pier column have a significant effect on the spatial and temporal distributions of the bed friction velocity induced by the horseshoe vortex system. The large-scale shedding behind the main column greatly influences flow structure and increases bed friction velocity around the downstream column for piers with two back-to-back columns that are aligned with the incoming flow direction. The present study shows that the presence of large-scale unsteady coherent structures in the vicinity of the bed around piers of complex shapes results in very complex distributions of the bed friction velocity and in large-scale temporal oscillations of the bed friction velocity. The results of eddy-resolving simulations strongly suggest the need to account for the effect of these large-scale oscillations around the mean value when bed friction velocity distributions are used to estimate the flux of entrained sediment in movable bed simulations that do not resolve the large-scale turbulent flow structures.

Validation of transport and friction formulae for upper plane bed by experiments in rectangular pipe

Abstract The paper describes results of validation of authors' recently proposed formulae for sediment transport and bed friction in the upper plane bed regime using laboratory experiments in a pressurized pipe. Flows of mixture of water and fine to medium ballotini (d50 = 0.18 mm) were observed in a rectangular pipe (51 x 51 mm) with a deposit at the bottom of the pipe. A comparison of test results with transport-formula predictions shows a satisfactory match confirming a good prediction ability of the proposed transport formula at high bed shear. A prediction ability of the friction formulae appears to be less convincing but still reasonable. A joint use of the formulae for transport and friction predicts the delivered concentration of transported sediment within the accuracy range of ± 40 per cent for flows in which transported sediments strongly affect the bed friction, i.e. for flows with delivered concentration of sediment higher than say 3 per cent.

Sea level rise and tidal power plants in the Gulf of Maine

The response of the Bay of Fundy and Gulf of Maine to large‐scale tidal power plants and future sea‐level rise is investigated using an established numerical tidal model. Free stream tidal turbines were simulated within the Bay of Fundy by implementing an additional bed friction term, Kt. The present‐day maximum tidal power output was determined to be 7.1 GW, and required Kt = 0.03. Extraction at this level would lead to large changes in the tidal amplitudes across the Gulf of Maine. With future SLR implemented, the energy available for extraction increases with 0.5–1 GW per m SLR. SLR simulations without tidal power extraction revealed that the response of the semidiurnal tides to SLR is highly dependent on how changes in sea level are implemented in the model. When extensive flood defenses are assumed at the present‐day coast line, the response to SLR is far larger than when land is allowed to (permanently) flood. For example, within the Bay of Fundy itself, the M2 amplitude increases with nearly 0.12 m per m SLR without flooding, but it changes with only 0.03 m per m SLR with flooding. We suggest that this is due to the flooding of land cells changing the resonant properties of the basin.

An improved method for applying the lockhart–martinelli correlation to three‐phase gas–liquid–solid horizontal pipeline flows

AbstractThree‐phase (G/L/S) horizontal pipe flow data collected from the literature are used to evaluate the performance of a number of correlations designed to predict the pipeline pressure gradient. In the present study, a number of popular two‐phase gas–liquid pressure loss correlations were modified for three‐phase flow predictions. The primary modification is to assume that the slurry (L/S) mixture behaves as a singlephase. The modified Dukler and the Beggs and Brill correlations did not provide accurate estimates of the three‐phase pressure gradients. When the classical Lockhart–Martinelli (L–M) correlation was used, along with a kinematic friction loss model to calculate the slurry (L/S) superficial flow pressure gradient, accurate predictions of the three‐phase (G/L/S) pressure gradient were obtained provided the slurry did not exhibit non‐Newtonian behaviour and that Coulombic (sliding bed) friction was negligible. Additional experiments should be conducted before the improved version of the L–M correlation is applied to commercial installations with pipe diameters greater than 100 mm.

LES of lock-exchange compositional gravity currents: a brief review of some recent results

Three-dimensional 3-D Large eddy simulation (LES) has become a powerful tool to investigate evolution and structure of gravity currents, especially for cases (e.g., high Reynolds number flows, flows with massive separation) where 3-D Direct numerical simulation using non-dissipative viscous solvers is computationally too expensive. In this paper we briefly review some important results obtained based on high-resolution 3-D LES of bottom-propagating compositional Boussinesq currents in lock-exchange configurations. LES was used to provide a detailed description of the structure of the current, to discuss the role of the large-scale coherent structures, and to predict the evolution of the front velocity over the different stages of the current propagation. Three main types of lock-exchange flows are considered: (1) currents with a high volume of release (HVR) and a low volume of release (LVR) propagating in a channel with a smooth horizontal bed; (2) HVR and LVR currents propagating in a horizontal channel containing a porous layer; and (3) currents propagating in a horizontal channel containing an array of bottom obstacles (2-D dunes and ribs). The simulations are performed using non-dissipative numerical algorithms and sub-grid scale models that predict a zero eddy viscosity in regions where the turbulence is negligible. Experimental data is used to validate LES predictions. LES results show that in most cases the evolution of the front velocity is consistent with that predicted based on shallow-flow theory. LES flow fields are then used to estimate important quantities (e.g., bed friction velocity, sediment entrainment capacity) that are very difficult to obtain from experiments and to understand how the structure and evolution of the current change because of the additional drag induced by obstacles present within the channel or at the channel bed. The paper also discusses how the evolution and structure of the current change as the Reynolds number is increased to values that are relevant for gravity currents encountered in geosciences and environmental engineering applications.

Flume experiments on entrainment of large wood in low-land rivers

ABSTRACTFloating wood is increasingly recognized as a source of hazard during flood events, because of its potential to clog bridges and hydraulic structures. However, wood entrainment by water is not well understood and only few studies addressing this issue are published. This paper reports on laboratory tests that were performed in a straight flume with fixed bed on logs with different shapes, orientations and densities. The logs oriented parallel to the water flow moved by sliding at undisturbed water depths larger than their buoyant depths, which was due to significant lowering of the water level around the log. Our analyses demonstrate that the entrainment condition cannot be simply defined as a balance between bed friction and drag force. Instead, the flow around the logs should be taken into account, with inclusion of acceleration and streamline curvature. For reliable predictions more experimental data are needed, including the effects of a mobile bed.

Effect of string bed pattern on ball spin generation from a tennis racket

Topspin has become a vital component of modern day tennis. Ball-to-string bed and inter-string friction coefficients can affect topspin generation from a racket. The aim of this research was to determine the effect of string bed pattern on topspin generation. Tennis balls were projected onto nine head-clamped rackets with different string bed patterns. The balls were fired at 24 m/s, at an angle of 26° to the string bed normal with a backspin rate of 218 rad/s and outbound velocity, spin and angle were measured. Outbound velocity was shown to be independent of string bed pattern. Outbound angle increased with the number of cross strings, while outbound topspin decreased. In the most extreme case, decreasing the number of cross strings from 19 to 13 increased rebound topspin from 117 to 170 rad/s.