Analytical solution for vertical profile of streamwise velocity in open-channel flow with submerged vegetation
TL;DR: In this article, a three-zone model was constructed and applied to study vertical profiles of streamwise velocity in steady uniform, open-channel flows with submerged vegetation, where the dominant forces acting on the water body were mainly gravity, vegetation drag and Reynolds stress.
Abstract: A three-zone model was constructed and applied to study vertical profiles of streamwise velocity in steady uniform, open-channel flows with submerged vegetation. Three zones are examined—lower vegetation, upper vegetation and non-vegetated. Dominant forces acting on the water body were mainly gravity, vegetation drag and Reynolds stress. The latter was estimated by mixing length theory. A power series method was used to solve the governing differential equation of the upper vegetation zone. Other governing equations for the remaining two zones were directly solved analytically, deriving formulas for calculating the streamwise velocities. Values calculated with the formulas agreed well with measured experimental data, which demonstrates the practical applicability of the model.
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TL;DR: In this article, the authors compared the performance of a large number of models on flow resistance, vegetation drag, vertical velocity profiles and bed-shear stresses in vegetated channels.
Abstract: The presence of vegetation modifies flow and sediment transport in alluvial channels and hence the morphological evolution of river systems. Plants increase the local roughness, modify flow patterns and provide additional drag, decreasing the bed-shear stress and enhancing local sediment deposition. For this, it is important to take into account the presence of vegetation in morphodynamic modelling. Models describing the effects of vegetation on water flow and sediment transport already exist, but comparative analyses and validations on extensive datasets are still lacking. In order to provide practical information for modelling purposes, we analysed the performance of a large number of models on flow resistance, vegetation drag, vertical velocity profiles and bed-shear stresses in vegetated channels. Their assessments and applicability ranges are derived by comparing their predictions with measured values from a large dataset for different types of submerged and emergent vegetation gathered from the literature. The work includes assessing the performance of the sediment transport capacity formulae of Engelund and Hansen and van Rijn in the case of vegetated beds, as well as the value of the drag coefficient to be used for different types of vegetation and hydraulic conditions. The results provide a unique comparative overview of existing models for the assessment of the effects of vegetation on morphodynamics, highlighting their performances and applicability ranges. Copyright © 2014 John Wiley & Sons, Ltd.
172 citations
Cites background from "Analytical solution for vertical pr..."
...A precise description is necessary for the understanding of the flow–sediment interaction (Hu et al., 2013)....
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...However, most of them require a layerthickness pre-definition or a calibration of length-scale related parameters (Huai et al., 2009; Hu et al., 2013)....
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TL;DR: In this article, an analytical model for predicting the vertical distribution of mean streamwise velocity in an open channel with double-layered rigid vegetation is proposed, and good agreement between the analytical predictions and experimental data demonstrated the validity of the model.
78 citations
Cites background or methods from "Analytical solution for vertical pr..."
...(4) [21,25]...
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...[21]....
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...This work is an extension of our previous work about the single-layered vegetation, and a power series method [21] was adopted in this paper....
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...While, for a submerged single layer vegetation flow, the streamwise velocity is almost constant near the bottom and gradually increases to the water surface [21,23]....
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...16, which is smaller than that for a single layer [21]....
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Journal Article•
TL;DR: In this paper, a 2D particle tracking velocimetry was used to explore aspects of the flow through and beneath suspended canopies constructed from rigid cylinders, and the experimental data showed that the penetration of the shear layer into the canopy is limited by the distance between the canopy and bottom boundary layer.
Abstract: Aquatic suspended canopies are porous obstacles that extend down from the free-surface but have a gap between the canopy and bed. Examples of suspended canopies include those formed by aquaculture structures or floating vegetation. The major difference between suspended canopies and the more common submerged canopies, which are located on the bottom boundary, is the influence of the bottom boundary layer beneath the suspended canopy. Data from laboratory experiments are presented which explore aspects of the flow through and beneath suspended canopies constructed from rigid cylinders. The experiments, using both acoustic Doppler and two-dimensional (2D) particle tracking velocimetry, give details of the flow structure that may be divided vertically into a bottom boundary layer, a canopy shear layer, and an internal canopy layer. The experimental data show that the penetration of the shear layer into the canopy is limited by the distance between the canopy and bottom boundary layer. Peaks in velocity spectra indicate an interaction between the bottom boundary and canopy shear layer. An analytical model is also developed that can be used to calculate a drag coefficient that includes the effect of both canopy drag and bed friction. This drag coefficient is suitable for use in 2D (depth-averaged) hydrodynamic modeling. The model also allows the average velocity within and beneath the canopy to be calculated, and is used to investigate the effect of canopy density and thickness on both total drag and bottom friction.
63 citations
TL;DR: In this article, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations.
Abstract: Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (
$$\partial \overline{u}/\partial z < 0$$
) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (
$$- \overline{{u^{\prime}w^{\prime}}} < 0$$
) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.
34 citations
Cites methods from "Analytical solution for vertical pr..."
...Similar to submerged vegetation flow with negligible lateral boundary influence [9, 16], the analytical solution for the Environ Fluid Mech (2016) 16:807–832 809...
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TL;DR: In this article, the most uncertain parameter in determining the stage-discharge relationship of an ungauged stream is the friction factor, a parameter for which a gauged stream can be back-calculated using hydrometric survey data that has been compiled over a wide range of flow conditions.
32 citations
References
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Book•
01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
TL;DR: In this article, a theory for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid is developed for the lower frequency range where the assumption of Poiseuille flow is valid.
Abstract: A theory is developed for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid. The emphasis of the present treatment is on materials where fluid and solid are of comparable densities as for instance in the case of water‐saturated rock. The paper denoted here as Part I is restricted to the lower frequency range where the assumption of Poiseuille flow is valid. The extension to the higher frequencies will be treated in Part II. It is found that the material may be described by four nondimensional parameters and a characteristic frequency. There are two dilatational waves and one rotational wave. The physical interpretation of the result is clarified by treating first the case where the fluid is frictionless. The case of a material containing viscous fluid is then developed and discussed numerically. Phase velocity dispersion curves and attenuation coefficients for the three types of waves are plotted as a function of the frequency for various combinations of the characteristic parameters.
7,172 citations
TL;DR: In this paper, the theory of propagation of stress waves in a porous elastic solid developed in Part I for the low-frequency range is extended to higher frequencies, and the breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes.
Abstract: The theory of propagation of stress waves in a porous elastic solid developed in Part I for the low‐frequency range is extended to higher frequencies. The breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes. As in Part I the emphasis of the treatment is on cases where fluid and solids are of comparable densities. Dispersion curves for phase and group velocities along with attenuation factors are plotted versus frequency for the rotational and the two dilational waves and for six numerical combinations of the characteristic parameters of the porous systems. Asymptotic behavior at high frequency is also discussed.
3,600 citations
TL;DR: In this paper, a unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived, including anisotropic media, solid dissipation, and other relaxation effects.
Abstract: A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid‐solid medium is treated as a complex physical‐chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.
3,450 citations
"Analytical solution for vertical pr..." refers methods in this paper
...To estimate the vertical velocity profile, a solution was derived by applying the theory of turbulent flow and Biot’s theory of poroelasticity [3,4]....
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TL;DR: In this paper, the transition between submerged and emergent regimes is described based on three aspects of canopy flow: mean momentum, turbulence, and exchange dynamics, and the observations suggest that flow within an aquatic canopy may be divided into two regions.
Abstract: Aquatic vegetation controls the mean and turbulent flow structure in channels and coastal regions and thus impacts the fate and transport of sediment and contaminants. Experiments in an open-channel flume with model vegetation were used to better understand how vegetation impacts flow. In particular, this study describes the transition between submerged and emergent regimes based on three aspects of canopy flow: mean momentum, turbulence, and exchange dynamics. The observations suggest that flow within an aquatic canopy may be divided into two regions. In the upper canopy, called the “vertical exchange zone”, vertical turbulent exchange with the overlying water is dynamically significant to the momentum balance and turbulence; and turbulence produced by mean shear at the top of the canopy is important. The lower canopy is called the “longitudinal exchange zone” because it communicates with surrounding water predominantly through longitudinal advection. In this region turbulence is generated locally by the canopy elements, and the momentum budget is a simple balance of vegetative drag and pressure gradient. In emergent canopies, only a longitudinal exchange zone is present. When the canopy becomes submerged, a vertical exchange zone appears at the top of the canopy and deepens into the canopy as the depth of submergence increases.
755 citations
"Analytical solution for vertical pr..." refers background in this paper
...There, exchange with surrounding water was mainly via vertical exchange, and vertical turbulent exchange with a non-vegetated region was dominant in the momentum balance and turbulence [27]....
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