Effects Of Bed Friction Research Articles

Application of Oversampling Techniques for Enhanced Transverse Dispersion Coefficient Estimation Performance Using Machine Learning Regression

The advection–dispersion equation has been widely used to analyze the intermediate field mixing of pollutants in natural streams. The dispersion coefficient, manipulating the dispersion term of the advection–dispersion equation, is a crucial parameter in predicting the transport distance and contaminated area in the water body. In this study, the transverse dispersion coefficient was estimated using machine learning regression methods applied to oversampled datasets. Previous research datasets used for this estimation were biased toward width-to-depth ratio (W/H) values ≤ 50, potentially leading to inaccuracies in estimating the transverse dispersion coefficient for datasets with W/H > 50. To address this issue, four oversampling techniques were employed to augment the dataset with W/H > 50, thereby mitigating the dataset’s imbalance. The estimation results obtained from data resampling with nonlinear regression method demonstrated improved prediction accuracy compared to the pre-oversampling results. Notably, the combination of adaptive synthetic sampling (ADASYN) and eXtreme Gradient Boosting regression (XGBoost) exhibited improved accuracy compared to other combinations of oversampling techniques and nonlinear regression methods. Through the combined ADASYN–XGBoost approach, it is possible to enhance the transverse dispersion coefficient estimation performance using only two variables, W/H and bed friction effects (U/U*), without adding channel sinuosity; this represents the effects of secondary currents.

A numerical model for predicting waves run-up on coastal areas

ABSTRACT In this study, numerical investigations are performed to validate a numerical model for the prediction of waves propagation and waves run-up on coastal zones. The proposed numerical model is based on the depth-averaged two-dimensional dispersive shallow water equations with source terms due to variable bottom topography and bed friction effects. We propose to solve the resulting nonlinear system using a well-balanced positivity preserving Godunov-type finite volume method on unstructured triangular grids. We used a semi-implicit scheme for the friction terms and a well-balanced formulation for the bottom topography. Moreover, we prove that the numerical scheme exactly preserves a class of nontrivial steady-state solutions. To validate the proposed numerical model against experiments, we first demonstrate its ability to preserve nontrivial steady-state solutions over a slanted surface and then we model several laboratory experiments for the prediction of waves run-up on sloping beaches. The numerical simulations are in good agreement with laboratory experiments which confirms the robustness and accuracy of the proposed numerical model in predicting waves propagation on coastal areas.

Depth-averaged simulation of flows in asymmetric compound channels with smooth and rough narrow floodplains

ABSTRACTDepth-averaged hydrodynamic models are predominantly used in numerical simulations of compound channel flows. One of the most popular methods for the depth-averaged simulation is Shiono and Knight method (SKM). This method accounts for the effects of bed friction, lateral turbulence and secondary flows, via three key parameters f, λ and Γ, respectively. The conventional expressions that are developed to calibrate these parameters are generally based on experiments in compound channels with wide floodplains. In this study, the application of SKM to an asymmetric compound channel with a narrow floodplain is examined in terms of the calibration requirements. Two sets of experiments that have smooth and rough floodplains are conducted and then simulated by SKM. In smooth floodplain cases, the results reveal that SKM model with the conventional calibration expressions of f, λ and Г is reasonably capable of predicting the distributions of depth-averaged velocity and boundary shear stress in the main channel. However, in the floodplain region, the expressions recommended for calibrating Г need to be modified to improve the predicted results in that region. In cases of the rough floodplain, the results indicate that only the values of λ in the main channel need to be changed from its conventional values to improve the predictions.

Combined effects of bed friction and emergent cylinder drag in open channel flow

Open channel flows subjected to a longitudinal transition in roughness, from bed friction to emergent cylinder drag and vice versa, are investigated experimentally in an 18 m long laboratory flume. These are compared to uniform flows subject to (1) bed roughness only and (2) an array of emergent vertical cylinders installed on bed roughness. The nearbed region is investigated in detail for uniform flows through the cylinder array. The water column can be divided into two parts: a region of constant velocity and a boundary layer near the channel bed. In the latter region, a local increase in velocity, or velocity bulge, is observed in line of a cylinder row. The velocity bulge may be related to the disorganization of the von Karman vortex street by the bed-induced turbulence, resulting in reduced momentum loss in the cylinder wake. The boundary layer height is found to be independent of water depth and bed roughness (smooth or rough bottom). Strong oscillations of the free surface (seiching) are observed. Oscillation amplitude is dependent on the longitudinal position within the cylinder array and is found to decrease with decreasing array length. When water depth/boundary layer height ratio is close to unity, the disorganization of the von Karman vortex street throughout the water column prevents seiching from occurring. In the case of roughness transition flows, the water depth is found to vary only upstream of the change in roughness. Vertical profiles of velocity and turbulence are self-similar upstream of the transition and collapse with the uniform flow profiles. Downstream of the roughness change, velocity and turbulence vary over a distance of 35 to 50 times the water depth. Roughness transition flows show that seiching is lowered by flow non-uniformity. A 1D momentum equation integrating bed friction and drag force exerted by the cylinder array predicts accurately the water surface profile (0.9% mean relative error). The computed profiles show that, upstream of the transition, flow depth varies over a distance of about 2600 times the uniform water depth of the upstream roughness. The 1D equation is solved analytically for zero bed friction.

An integral treatment of friction during a swash uprush

The effects of bed friction are modelled for the flow near the moving shoreline during the uprush phase of a swash event by extending the Pohlhausen method used by Whitham (1955) to a sloping bed. The tip of the swash near the moving shoreline is treated in an integral sense as a region of uniform velocity, being acted on by the forces of friction, gravity, and the pressure force induced by the frictionless flow behind the swash tip. The bed shear stress is parameterized by using the quadratic dependence on velocity. The theory is compared to data of the shoreline velocity and position in the swash of breaking solitary waves, and the friction coefficient is determined from direct measurements of bed shear stress. The theoretical predictions are in good agreement with the laboratory results in terms of time history of the shoreline velocity and position, as well as the run-up.

Discrete mixed subdomain least squares (DMSLS) meshless method with collocation points for modeling dam-break induced flows

This paper presents a new meshless numerical scheme to overcome the problem of shock waves and to apply boundary conditions in cases of dam-break flows in channels with constant and variable widths. The numerical program solves shallow water equations based on the discrete mixed subdomain least squares (DMSLS) meshless method with collocation points. The DMSLS meshless method is based on the minimization of a least squares functional defined as the weighted summation of the squared residuals of the governing equations over the entire domain and requiring the summation of residual function to be zero at collocation points in boundary subdomains. The collocated discrete subdomain meshless method is applied on the boundary, whereas the collocated discrete least squares meshless technique is applied to the interior domain. The meshless scheme extends for dam-break formulation of shallow water equations. The model is verified by comparing computed results with analytical and experimental data for constant and varying width channels. The developed model is also used to study one-dimensional dam-break problems involving different flow situations by considering changes to the channel width, a bumpy channel with various downstream boundary conditions, and the effects of bed friction and bed slope as source terms on wave propagation. The accuracy of the results is acceptable.

The lateral distribution of depth-averaged velocity in a channel flow bend

This paper proposes an analytical model to predict the lateral distribution of streamwise velocity for flow in a curved channel with vertical sides, based on the depth-integrated Navier–Stokes equations. The model includes the effects of bed friction, lateral turbulence and secondary flows, where the additional secondary flow is approximated by a linear function of the lateral distance, as demonstrated by the limited data which are available. Two analytical solutions for the depth-averaged velocity are obtained, one for a flat bed and another for a bed with a transverse slope. Two parameters (denoted by m and n herein), which define the secondary flow, have been examined to analyze how they affect the velocity distribution in these two cases. Comparison of the analytical results with the limited experimental data available shows that the proposed model predicts the lateral distributions of depth-averaged velocity well. Further studies are needed to validate the values of the model parameters (m and n) for bends with different geometric properties.

Predictive model for stage-discharge curve in compound channels with vegetated floodplains

The governing equation of the discharge per unit width, derived from the flow continuity equation and the momentum equation in the vegetated compound channel, is established. The analytical solution to the discharge per unit width is presented, including the effects of bed friction, lateral momentum transfer, drag force, and secondary flows. A simple but available numerical integral method, i.e., the compound trapezoidal formula, is used to calculate the approximate solutions of the sub-area discharge and the total discharge. A comparison with the published experimental data from the U. K. Flood Channel Facility (UK-FCF) demonstrates that this model is capable of predicting not only the stage-discharge curve but also the sub-area discharge in the vegetated compound channel. The effects of the two crucial parameters, i.e., the divided number of the integral interval and the secondary flow coefficient, on the total discharge are discussed and analyzed.

Fourier analysis of the roll-up and merging of coherent structures in shallow mixing layers

The current study investigates the role of nonlinearity in the development of two-dimensional coherent structures (2DCS) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate temporal shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layer. The flow is periodic in the stream-wise direction and the transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. The numerical results are examined with the aid of Fourier decomposition. Results show that the previous success in applying local linear theory to shallow mixing layers does not imply that the flow is truly linear. Linear stability theory is confirmed to be only valid within a short distance from the inflow boundary. Downstream of this linear region, nonlinearity becomes important for the roll-up and merging of 2DCS. While the energy required for the merging of 2DCS is still largely provided by the velocity shear, the merging mechanism is one where nonlinear mode interaction changes the velocity field of the subharmonic mode and the gradient of the along-stream velocity profile which, in turn, changes the magnitude of the energy production of the subharmonic mode by the velocity shear implicitly. The nonlinear mode interaction is associated with energy up-scaling and is consistent with the inverse energy cascade which is expected to occur in shallow shear flows. Current results also show that such implicit nonlinear interaction is sensitive to the phase angle difference between the most unstable mode and its subharmonic. The bed friction effect on the 2DCS is relatively small initially and grows in tandem with the size of the 2DCS. The bed friction also causes a decrease in the velocity gradient as the flow develops downstream. The transition from unstable to stable flow occurs when the bed friction balances the energy production. Beyond this point, the bed friction is more dominant and the 2DCS are progressively damped and eventually get annihilated. The energy production by the velocity shear plays an important role from the upstream end all the way to the point of transition to stable flow. The fact that linear stability theory is valid only for a short distance from the inflow boundary suggests that some elements of nonlinearity is incorporated in the mean velocity profile in experiments by the averaging process. The implicit nature of nonlinear interaction in shallow mixing layers and the sensitivity of the nonlinear interaction to phase angle difference between the most unstable mode and its subharmonic allows local linear theory to be successful in reproducing features of the instability such as the dominant mode of the 2DCS and its amplitude.

Determining drag coefficients and their application in modelling of turbulent flow with submerged vegetation

Vegetation is a key aspect of water resources and ecology in natural rivers, floodplains and irrigation channels. The hydraulic resistance of the water flow is greatly changed when submerged vegetation is present. Three kinds of drag coefficients, i.e., the drag coefficient for an isolated cylinder, the bulk drag coefficient of an array of cylinders and the vertically distributed or local drag coefficient, have been commonly used as parameters to represent the vegetation drag force. In this paper, a comprehensive experimental study of submerged stems in an open channel flow is presented. Empirical formulae for the three drag coefficients were obtained based on our experimental results and on data from previous studies. A two-layer model was developed to solve the mean momentum equation, which was used to evaluate the vertical mean velocity profile with each of the drag coefficients. By comparing the velocity distribution model predictions and the measurement results, we found that the model with the drag coefficient for an isolated cylinder and the local drag coefficient was good fit. In addition, the model with the bulk drag coefficient gave much larger velocity values than measurements, but it could be improved by adding the bed friction effect and making choice of the depth-averaged velocity within the canopy layer.

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.

Suspension and near‐bed load sediment transport processes above a migrating, sand‐rippled bed under shoaling waves

The present study focuses on the fine‐scale flow and sand transport processes above onshore migrating ripples below skewed surface gravity waves in the shoaling zone. A set of acoustic instruments was deployed in the shoaling region of the large‐scale wave channel at Canal d'Investigacío i Experimatacío Marítima, Universitat Poltiècnica de Catalunya, Barcelona, Spain, in order to provide high‐resolution velocity and sediment concentration profiles with an acoustic concentration and velocity profiler (ACVP). Measurements are analyzed relative to the positions of the measured nonmoving sand bed and the interface separating the suspension from the near‐bed load layer. This interface is detected here by the application of a novel acoustic bed echo detection method. Furthermore, the use of the dual‐frequency inversion proposed in the work of Hurther et al. (2011) allows for the calculation of the sediment concentration profile across both the suspension and near‐bed load layers. The sand bed was covered by quasi‐two‐dimensional suborbital ripples migrating onshore. As proposed by O'Donoghue et al. (2006), the occurrence of quasi‐two‐dimensional ripples is attributed to the fine‐size sand ofD50= 250μm used in the present study under full‐scale forcing conditions. In order to determine the effect of shoaled wave skewness on the ripple vortex entrainment and sediment transport, the instantaneous and mean measurements of the flow, sediment concentration, and sediment flux along the ripple profile are discussed in terms of (1) the occurrence of ripple vortex entrainment on either side of the ripple crest; (2) the wave velocity phase lagging driven by the ripple vortex entrainment process and the turbulent bed friction effects in the wave boundary layer; (3) phase lagging between velocity and maximum concentration and sediment flux events; (4) the structure of bed friction and ripple‐driven turbulence across the suspension and the near‐bed load layers; and (5) the streaming components. The results on these aspects strongly support that the wave velocity skewness effect under shoaling waves is fairly similar to the one obtained in skewed oscillatory water tunnel flows. Furthermore, it is found that the onshore‐oriented net bed load sediment transport is at the origin of the onshore ripple migration. This flux is roughly twice as much as the opposite offshore‐oriented net suspension flux dominated by the ripple vortex entrainment processes.

Analytical model for streamwise velocity in vegetated channels

This paper presents a method for predicting the lateral distribution of depth-averaged streamwise velocity in straight prismatic open channels with emergent vegetation. The approach is fully consistent with the original Shiono and Knight method of analysis, and extends it to include the drag force due to vegetation, modelled as an additional momentum ‘sink' term, with the blockage effect of the vegetation modelled by way of a porosity analogy. An analytical solution to the depth-integrated Reynolds-averaged Navier–Stokes equation is given which includes the effects of bed friction, drag force, lateral turbulence and secondary flows, governed by four coefficients f, CD, λ and Γ respectively. The analytical results are shown to predict the lateral distributions of depth-averaged velocity well for three sets of experimental data: one for inbank flow in a partially vegetated channel and two for overbank flows in compound channels with partially vegetated floodplains. The analytical solution is also shown to give identical results to numerical simulations of the same governing Reynolds-averaged Navier–Stokes equation applied to some experiments undertaken in the UK Flood Channel Facility. The lateral distribution of bed shear stress is also obtained through the Darcy–Weisbach friction factor, thus providing a basis for modelling flood conveyance, fluvial processes and eco-environmental impacts in natural rivers.

The Effects of Bed Friction on Wave Simulation: Implementation of an Unstructured Third-Generation Wave Model, SWAN

Abstract Parallel implementation of an unstructured Simulating Waves Nearshore (SWAN) model with the Wave Model (WAM) cycle 4 formulation was used to evaluate the performance of a third-generation wave model over large spatial scales. Data from a network of National Data Buoy Center (NDBC) buoys and the Wave Current Information System (WAVCIS) stations were used to assess the skill of the input and output of the wave model. The simulation results reveal that the underestimation of energy in the low-frequency band (0.12–0.17 Hz) can be ameliorated if the model is calibrated using site specific in situ measurements instead of the Pierson-Moskowitz spectra. This process led to more than a 25% decrease in the root mean square error between simulated significant wave height and in situ observations. Use of the verified model for the Gulf of Mexico, with bed friction computed from grain-size distribution, as opposed to a default constant bed-friction formulation, showed that the wave height difference can excee...

Lateral distributions of streamwise velocity in compound channels with partially vegetated floodplains

Natural rivers are commonly characterized by a main channel for primary flow conveyance and a floodplain, often partially covered with vegetation such as shrubs or trees, to carry extra flow during floods. The hydraulic resistance due to vegetation on the floodplain typically causes a further reduction of flow velocity and increases the velocity difference between the main channel and the floodplain. As a consequence a strong lateral shear layer leads to the exchange of mass and momentum between the main channel and floodplain, which in turn affects the overall channel conveyance and certain fluvial processes. The prediction of the lateral velocity distribution is important for many flood alleviation schemes, as well as for studies on sediment transport and dispersion in such channels. The present paper proposes a method for predicting the depth-averaged velocity in compound channels with partially vegetated floodplains, based on an analytical solution to the depth-integrated Reynolds-Averaged Navier-Stokes equation with a term included to account for the effects of vegetation. The vegetation is modelled via an additional term in the momentum equation to account for the additional drag force. The method includes the effects of bed friction, drag force, lateral turbulence and secondary flows, via four coefficients f, CD, λ & Γ respectively. The predicted lateral distributions of depth-averaged velocity agree well with the experimental data. The analytical solutions can also be used to predict the distribution of boundary shear stresses, which adds additional weight to the method proposed.

Analytical models for velocity distributions in open channel flows

Various models for the analytical solution to the depth-integrated Navier-Stokes equations, applied to open channel flows, are discussed. These models include the effects of bed friction, lateral turbulence and secondary flows. The model developed by Shiono and Knight (1988, 1991) is compared with those by Ervine et al. (2000) and Castanedo et al. (2005) through numerical experiments on both simple and compound channels. These tests show that the impact of the secondary flow term on the results is significant. It is also shown that the dimensionless eddy viscosity coefficient has less influence on the results than the secondary flow terms for overbank flows, but is important for inbank flows. A comparison of the analytical results with experimental data shows that the model by Shiono and Knight produces well velocity distributions within open channels of various prismatic shapes.

Lateral Depth-Averaged Velocity Distributions and Bed Shear in Rectangular Compound Channels

This paper presents a method to predict depth-averaged velocity and bed shear stress for overbank flows in straight rectangular two-stage channels. An analytical solution to the depth-integrated Navier–Stokes equation is presented that includes the effects of bed friction, lateral turbulence, and secondary flows. The Shiono and Knight method accounts for bed shear, lateral shear, and secondary flow effects via three coefficients, f , λ , and Γ , respectively. A novel boundary condition at the internal wall between the main channel and the adjoined floodplain is proposed and discussed along with other conventional boundary conditions. The analytical solution using the novel boundary condition gives good prediction of both lateral velocity distribution and bed shear stress when compared with experimental data for different aspect ratios.

Zonal discharges and boundary shear in prismatic channels

This paper illustrates a new approach to obtaining analytical stage–discharge formulae for both zonal and total discharges in straight prismatic channels of any shape, based on the concepts of a zero–shear force interface and an analytical solution for the lateral variation of depth-averaged velocity. The analytical solution for velocity is derived from the depth-integrated form of the Navier–Stokes equations, and includes the effects of bed friction, lateral turbulence, and secondary flows/planform vorticity. The analytical formulae for stage discharge are given for both simple and compound trapezoidal channels, together with formulae that permit the boundary shear force to be determined for every linear element on the wetted perimeter. These stage–discharge and shear force formulae depend on the channel geometry and on three hydraulic parameters related to the bed friction factor f, lateral eddy viscosity λ and depth-averaged secondary flow Γ, as required in the original Shiono and Knight method. The analytical results show good agreement with experimental data. Ways of extending this approach to more complex shaped channels are outlined.

Bed friction effects on the stability of a stationary hydraulic jump in a rectangular upward sloping channel

The issue of the bed friction effect on the stability of a stationary hydraulic jump in a rectangular upward sloping channel is investigated through a combined theoretical and experimental approach. The theoretical stability criterion proposed by Defina and Susin [Phys. Fluids 15, 3883 (2003)] is generalized to include rough wall flows. The results of an extensive series of experiments are then presented. The adopted experimental procedure is detailed, and results are compared with theoretical predictions. It is shown that the proposed stability criterion successfully predicts both the stable and unstable behavior of the jump for smooth and rough wall flow, at least in the range of small upward bottom slopes.

A general model of lateral depth-averaged velocity distributions for open channel flows

This paper reviews a model, developed by Shiono and Knight [Shiono K, Knight DW. Two-dimensional analytical solution for a compound channel. In: Proceedings of the 3rd international symposium on refined flow modelling and turbulence measurements, Tokyo, Japan, July 1988. p. 503–10; Shiono K, Knight DW. Turbulent open channel flows with variable depth across the channel. J Fluid Mech 1991;222:617–46 [231:693]], which yields analytical solutions to the depth-integrated Navier–Stokes equations, and includes the effects of bed friction, lateral turbulence and secondary flows. Some issues about the original model developed by Shiono and Knight (1988, 1991) are highlighted and discussed. Based on the experimental data concerning the secondary flow, two assumptions are proposed to describe the contribution of the streamwise vorticity to the flow. Two new analytical solutions are compared with the conventional solution for three simple channel shapes and one trapezoidal compound channel to highlight their differences and the importance of the secondary flow and planform vorticity term. Comparison of the analytical results with the experimental data shows that the general SKM predicts the lateral distributions of depth-averaged velocity well.