Movable Bed Research Articles

Applicability of the De Marchi Hypothesis for Side Weir Flow in the Case of Movable Beds

Side weirs are widely used hydraulic structures typically designed and studied in the case of fixed bed conditions. In the case of subcritical flows, the hydraulics of side weirs can be modelled by using the classical De Marchi hypothesis. In the present work, a generalization of this hypothesis is developed for the case of side weirs over movable beds. Experiments showing the effects and feedbacks between the spilling discharge and the bed morphodynamics are presented. The application of the experimental observations to the generalized De Marchi hypothesis clearly show that the functioning of side weirs on a movable bed can be modelled by using this hypothesis. These findings could be instrumental for the design and verification of these structures. DOI: 10.1061/(ASCE)HY.1943-7900.0000566. © 2012 American Society of Civil Engineers. CE Database subject headings: Weirs; Experimentation; Channel flow; Movable bed models. Author keywords: Weirs; Subcritical flow; Experimentation; Channel flow.

Transport capacity models for unsteady and non-equilibrium sediment transport in alluvial channels

This study investigates transport capacity models based on different dominant variables-shear stress, stream power, unit stream power, flow discharge, flow velocity, and energy slope – in a model of unsteady and non-equilibrium sediment transport in alluvial channels. The model simulates fully coupled system of water flow, suspended sediment, and bed load sediment transport processes in two-layer system of water flow phase and movable bed. The model employs conservation of mass equation for the water in both the layers; suspended sediment in the water flow phase; sediment in the movable bed layer; and the momentum equation for the water flow in the flow phase. The system is closed by relating the sediment flux in the movable bed layer to the sediment concentration in the same layer by employing the kinematic wave theory. Using the sediment transport capacity expression with different dominant variables, a series of numerical experiments are carried out for unsteady and non-equilibrium sediment transport. The results seem theoretically reasonable for hypothetical cases. The model is calibrated and validated using different experimental data sets. The calibrated value for the transport capacity model’s exponent (ki) is found to be 1.50, 1.65, 0.24, 0.56, 4.80, and 0.22 for shear stress, stream power, unit stream power, discharge, velocity, and slope approaches, respectively. The numerical investigation results show that transport capacity model based on any dominant variable can be employed for modelling unsteady and non-equilibrium sediment transport.

固定床上に設置した水制周りの流れと流砂・河床変動特性

Spur dikes were expected to create new aquatic habitats according to produce local scour and sediment deposition area around them on the movable bed. However, when the spur dikes were set on the rigid bed for creating new aquatic habitats, it was not known the potential ability to accumulate sediment deposition behind spur dikes. In this study, we conducted experimental flume tests and numerical analysis to confirm the characteristics of flow, sediment transport and bed deformation around the spur dikes on the rigid bed. These results showed that the sediment was not deposited behind the spur dikes, because the sheer stress is smaller than the critical sheer stress in the upstream area of the spur dikes, so that all bed materials were transported to the opposite bank side. However, when the flow is under unsteady condition, it is confirmed that the no sediment transport area is reduced because the large transverse water surface gradient is formed in the downstream area of the spur dikes during the increase process of water discharge and would change the direction of sediment transport material.

Effects of the Central Bar Protection with Tetrahedron-like Penetrating Frames

The movement of the flow and sediment around a central bar is very complex, which will restrict the navigation development. The tetrahedron-like penetrating frames is always used for the flood and bank protection. The main objective of this study is to investigate the effects of central bar protection with the tetrahedron-like penetrating frames .Based on the analysis of the evolution of the typical reach of the central bar, experiment of the flume generalized model was carried out. Combining with the theoretical analysis, the variation regularity of the sediment-carrying capacity of flow and the movable bed resistance and the roughness of the beach face around the model central bar was compared before and after it was protected by the tetrahedron-like penetrating frames. The results show that the tetrahedron-like penetrating frames can protect the central bar better, which provides a new approach for beach protection.

急勾配リーフ上のサンゴ礁州島形成メカニズムに関する研究

Coral cays may be formed by the high waves in about several days. If the initial formation mechanism of coral cays can be understood, it will be useful for protection, the environmental preservation, and use of the coral reef seashore. Moreover, it can contribute also to protection of islands in Japan and the Pacific Ocean archipelagic country where the sea level rise due to global warming may result in submersion. In the past research, the formation mechanism of coral cays is performed by 2-dimensional tests. But, it includes neither the influence of 3-dimensional wave and current which were caused by waves equipped with open sea, nor the influence of a steep slope reef. In this paper, 3-dimensional hydraulic movable bed model tests were conducted to clarify the coral cays formation process.

Laboratorial studies on the seepage impact in open-channel flow turbulence

In natural streams, the interaction between water in motion and movable beds derives in transport of material. This is a fact that causes several problems for river regulation, above all in streams which were heavily modified by human interferences. Therefore, to find solutions or at least to alleviate the negative effects that sediment transport can bring with is a topic to be researched. The impact of seepage on river sedimentation processes and open-channel flow is important for environmental issues but it is commonly neglected by water specialists. The present contribution presents the output of a series of experimental works where the influence of seepage on the open channel turbulence is analyzed at the laboratory scale. Even though that the magnitude of the groundwater flow is significantly smaller than the magnitude of the open channel flow; the output of the experiments demonstrates that seepage not only modifies the water-sediment interaction as demonstrated Herrera Granados (2008; 2010); but also is affecting the velocity field and turbulence dynamics of the open-channel flow.

Similarity Laws of Distorted Model with a Movable Bed and its Validity

The theoretical backing of the similarity laws obtained from dual dimensionless parameters of the bed-form classification diagram is given by solving the equations of similarity conditions which is obtained from 1-Dimensional equation of motion, continuity equation, bed deformation equation and the formula of bed load transport. Secondly, the validity of the similarity laws is confirmed by comparing the bed form of distorted model experiment with that of undistorted model experiments performed by Hokkaido Development Bureau (H.D.B.). And also the fact that the height of bar in a gentle curved river channel can be estimated by the result of distorted model of straight flume is found.

하도육역화 관리를 위한 물골의 수리학적 특성 분석

Laboratory experiments were carried out to analyze the hydraulic characteristics of the sub-channel in the flood plain able to manage landforming process. Hydraulic analysis was conducted based on the measurement of mean velocities and turbulent intensities along the sub-channel in the flood plain including the change of an inflow angle. Quantitative characteristics of inflow into the sub-channel in the flood plain were estimated by mean velocities and velocity vectors around the sub-channel in the flood plain obtained using LSPIV. The capacity of sediments flushing in the sub-channel in the flood plain was evaluated with turbulent intensities and friction velocities. It was found that when the elevation of free surface was higher than that of floodplain, the effect of sediments flushing through the sub-channel in the flood plain was not much effective, while it became much effective when the elevation of free surface descended below that of floodplain. In the case of rivers confluence, a conveyance of river branch increases with the increase of an angle of inflow. However, in the case of the sub-channel in the flood plain, the case of inflow angle of was the most effective to flush sediments inside the Mugol because turbulent intensity, friction velocity and unit conveyance became higher than other cases. Results from this study can be used to establish the design guidelines for the sub-channel in the flood plain. In near future, more laboratory experiments conducted with movable bed and fields monitoring would be provided much reliable quantitative analysis of sediments flushing in the sub-channel in the flood plain to resist landforming.

Promoting siltation effects and impacts of Hengsha East Shoal on the Yangtze River Estuary

For the Hengsha East Shoal Promoting Siltation Project in the Yangtze River Estuary, this work developed a formula for calculating sediment carrying capacity based on variable coefficients and a mathematical model for suspended sedimentation using variable saturation recovery coefficients. Not only does the model yield good verification, preferably give the hydrodynamics and the sediment concentration, but also reach a good agreement between the simulation results and the measured topographical changes in the promoting siltation zone of the Hengsha East Shoal. Moreover, this article proposes a method for examing the net sediment transportation flux by tide for studying the effects of the project of promoting siltation and comparatively analyzes the current siltation of the Hengsha East Shoal and siltation mouth layouts, entrance widths, entrance bottom elevations, and the impact of the South Main Dike on promoting siltation through calculating the net sediment transportation flux by tide over the fixed bed and the direct movable bed numerical simulations. The results are in good agreement with each other, indicating that the method for calculating the net sediment transportation flux by the tide is also useful for assessing the project in promoting siltation. Finally, we use the modeling results to analyze the water and sediment diversion ratios and the changes in silting and scouring in riverbeds and draw the conclusion that the completion of the Hengsha East Shoal Promoting Siltation Project would not adversely affect the Yangtze River Estuary Deepwater Channel Project.

Observations on undular hydraulic jump in movable bed

Near-critical flows in rivers and natural streams usually present a wavelike undular free surface, associated with dune-type bed-forms. The formation of this particular bed geometry is related to the shear stress acting on the river bed. The boundary shear stress distribution of undular flows was considered by Engelund and Hansen, stating that standing waves and their associated non-uniform shear stresses are responsible for bed-form generation in rivers. However, observations on movable-bed channels involving transcritical flow were not considered. In this note, an exploratory analysis is conducted to outline the analogy between the boundary shear in fixed-bed undular flows and the bed-form shape. Experimental observations reveal a strong analogy, supporting the original hypothesis of Engelund and Hansen.

Validation of a new generation system for bottom boundary layer beneath solitary wave

Understanding of sea bottom boundary layer characteristics, especially bottom shear stress acting on the sea bed, is an important step needed in sediment transport modeling for practical application purposes. In the present study, a new generation system for bottom boundary layer under solitary wave is proposed. Applicability of this system is examined by comparing measured and numerical solution velocities. Moreover, transitional behavior from laminar to turbulence was investigated. It is concluded that the critical Reynolds number in the experiments shows good agreement with DNS result of Vittori and Blondeaux (2008) and laboratory data of Sumer et al. (2010), indicating validity of the generation system. Since the present generation system enables continuous measurement to obtain ensemble averaged quantities, it can be effectively utilized for future experimental studies on solitary wave boundary layers, including sediment transport experiments with movable bed.

Wave–current interaction at an angle 1: experiment

This research presents an experimental study in a spatial wave basin for nonlinear interaction of regular waves with a perpendicular shear current over a movable bed. Detailed measurements were collected for current velocity profiles under different conditions, from which the bed shear stress and apparent roughness heights were determined. These combined with the measured velocities were used to validate theoretical models for wave–current interaction at an angle. It is found that for small wave heights all models agree well with the measured mean current velocities in the combined flow, while for larger wave heights only two models are reasonably close to the measurements for current velocities. For very large waves none of the models adequately describes the near-surface current velocities, which deviate significantly from the log-law. For the bed shear stress and the apparent roughness, only one model describes the measured data well.

HLLC scheme with novel wave‐speed estimators appropriate for two‐dimensional shallow‐water flow on erodible bed

AbstractThis paper presents a first‐order HLLC (Harten‐Lax‐Van Leer with contact discontinuities) scheme to solve the Saint‐Venant shallow‐water equations, including morphological evolution of the bed by erosion and deposition of sediments. The Exner equation is used to model the morphological evolution of the bed, while a closure equation is needed to evaluate the rate of sediment transport. The system of Saint‐Venant–Exner equations is solved in a fully coupled way using a finite‐volume technique and a HLLC solver for the fluxes, with a novel wave‐speed estimator adapted to the Exner equation. Wave speeds are usually derived by computing the eigenvalues of the full system, which is highly time‐consuming when no analytical expression is available. In this paper, an eigenvalue analysis of the full system is conducted, leading to simple but still accurate wave‐speed estimators. The new numerical scheme is then tested in three different situations: (1) a circular dam‐break flow over movable bed, (2) an one‐dimensional bed aggradation problem simulated on a 2D unstructured mesh and (3) the case of a dam‐break flow in an erodible channel with a sudden enlargement, for which experimental measurements are available. Copyright © 2010 John Wiley & Sons, Ltd.

1D finite volume model of unsteady flow over mobile bed

Summary A one dimensional (1D) finite volume method (FVM) model was developed for simulating unsteady flow, such as dam break flow, and flood routing over mobile alluvium. The governing equation is the modified 1D shallow water equation and the Exner equation that take both bed load and suspended load transport into account. The non-equilibrium sediment transport algorithm was adopted in the model, and the van Rijn method was employed to calculate the bed-load transport rate and the concentration of suspended sediment at the reference level. Flux terms in the governing equations were discretised using the upwind flux scheme, Harten et al. (1983) (HLL) and HLLC schemes, Roe’s scheme and the Weighted Average Flux (WAF) schemes with the Double Minmod and Minmod flux limiters. The model was tested under a fixed bed condition to evaluate the performance of several different numerical schemes and then applied to an experimental case of dam break flow over a mobile bed and a flood event in the Rillito River, Tucson, Arizona. For dam break flow over movable bed, all tested schemes were proved to be capable of reasonably simulating water surface profiles, but failed to accurately capture the hydraulic jump. The WAF schemes produced slight spurious oscillations at the water surface and bed profiles and over-estimated the scour depth. When applying the model to the Rillito River, the simulated results generally agreed well with the field measurements of flow discharges and bed elevation changes. Modeling results of bed elevation changes were sensitive to the suspended load recovery coefficient and the bed load adaptation length, which require further theoretical and experimental investigations.

Experimental investigation on the local scour characteristics around groynes using a hydraulic model

AbstractScour holes resulting from the installation of a groyne are considered to perform the environmental function of providing a habitat and a haven for various aquatic organisms during floods, hence, the need for studies on the scour area and its volume near a groyne beyond the scope of past discussions on their stability. In this study, hydraulic experiments were conducted in fixed and movable beds to examine the flow pattern, bed change and scour depth and hole around a groyne. The results of the fixed‐bed experiment indicated an effect on the flow change in the main channels and recirculation zones following the installation of a groyne. Changes in tip velocity and flow angle as the scour factors around a groyne were quantitatively compared as well. Through the movable‐bed experiment, the scour‐hole shape, scour area, scour depth and volume of bed change were examined and compared.

Three-Dimensional Modeling of Nonuniform Sediment Transport in an S-Shaped Channel

A three-dimensional numerical model was applied to compute uniform and nonuniform sediment transport and bed deformation in an S-shaped laboratory channel located at the University of Innsbruck, where detailed measurements of the velocity field and bed elevation changes were made. The channel had two bends, a trapezoidal cross section, and a slope of S=0.005. Gravel with a mean diameter of 4.2 mm was used as movable bed material and for sediment feeding. Wu’s formula for multiple grain sizes was compared with van Rijn’s formula using one grain size. Fairly good agreement was found between the computed and measured bed elevations for both approaches, whereas Wu’s formula could further improve the numerical results. Looking at the physics of the erosion pattern, the computed scour areas were located slightly more downstream than what was observed in the physical model. The current study also includes several parameter tests: grid distribution in vertical, lateral, and longitudinal direction; time step; number of inner iterations/time step; active sediment layer thickness; and the Shields coefficient. The variation of those parameters gave some differences in the results, but the overall pattern of bed elevation changes remained the same.

MODEL FOR PREDICTING FORMATION OF BAY BARRIER

A barrier island often develops along the marginal area of a flat shallow sea. Various explanations have been given for the cause of development of barrier islands. Most studies have focused on the development and deformation of a barrier island during increases in sea level in terms of the stratification of sand layers in the sand bar and the change in longitudinal profiles (Schwarz, 1971), and studies on the 3-D development of a barrier considering the water depth where the barrier island develops and wave intensity are rare. In this study, we consider the relationship between wave energy and the water depth where a barrier island develops, in which the wave energy reaching the shoreline is controlled under a constant-sea-level condition. On the basis of the results of a movable bed experiment by Uda et al. (1994), the development of a bay barrier is investigated using the BG model proposed by Serizawa et al. (2009), taking a bay barrier that extends deep in a bay as an example.

PREDICTING MOVABLE BED ROUGHNESS IN COASTAL WATERS

Accurately predicting movable bed roughness is essential to the analyses of transport processes, but when the bottom is rippled, as it commonly is in the coastal environment, characterizing the roughness is less straightforward than when the bottom is flat. The common method of predicting roughness, while effective, unnecessarily predicts ripple geometry and requires a model-dependent factor, which varies widely, relating ripple geometry and bottom roughness. We have therefore developed an alternative, more direct method of predicting bed roughness in the ripple regime: the wave energy dissipation factor is predicted from flow and sediment information and then any desired theoretical friction factor model is used to back-calculate the roughness. This paper describes the common and proposed methods of predicting roughness and presents results of preliminary testing of the methods with field data. Both methods adequately predict current velocities in wave-current field flows, with the proposed method yielding the smaller RMS-error of 3.1 cm/s. Remaining questions concerning the appropriate near-bottom orbital velocity required to describe field conditions must be resolved when additional field data becomes available.

ON THE BOTTOM SHEAR STRESS DURING LONG WAVE RUNUP AND BACKWASH

Laboratory experiments were performed to examine flow characteristics during runup and backwash of a breaking solitary wave. Boundary layer flows were measured by LDV at two locations landward of the still shoreline under different bed conditions. Temporal variations of the bottom shear stress were estimated from nearbed velocity profiles with different methods. The shear stress determined through the logarithmic fitting roughly agreed with that deduced from a depth-integrated momentum balance during turbulent flow phases. The friction factors during the active phases of the runup and backwash were similar in magnitude except in the leading tip where the value sharply increased. A movable bed experiment was also carried out under the same geometry to discuss relations between the bottom shear stress and sediment transport. The result indicated clear dependencies of bed deformations on the magnitude and duration of the exerted shear stress.

EXPERIMENTAL STUDY ON THE LOADING AND SCOUR OF THE JACKET TYPE OFFSHORE WIND TURBINE FOUNDATION

A 1:36 scale model tests were carried out in the Medium Wave Flume (MWF) and Near-shore Wave Basin (NSWB) at the Tainan Hydraulics Laboratory (THL) with the jacket type offshore wind turbine foundation located in the test area. The loading of typhoon wave with current on the jacket type offshore wind turbine foundation was investigated in the MWF with fixed bed experiment. Meanwhile, the scour around the jacket type offshore wind turbine foundation exposed to wave and current was conducted in the NSWB with the moveable bed experiment. Two locations (water depth 12m and 16m) of the foundations are separately simulated in this study. Based on the analysis from the former NSWB experimental results, the suitable scour protection of a four-layer work around the foundation is also proposed to the impact of scour. Finally, a four-layer scour protection is tested and found to be effective in preventing scour around jacket type foundation of offshore wind turbines at water depth 12m and 16m.