Hydraulics

=Hydraulics=


 * Introduction **

In this wiki, we will be discussing hydraulics and its application to water and river restoration. It is useful to provide a basic definition of hydraulics in its relation to this wiki’s application. Hydraulics is the branch of science concerned with the conveyance of liquids through pipes and channels, especially as a source of mechanical force or control. Two main topics will be discussed in this wiki: 1) the general principles of hydraulics and 2) hydraulics in stream restoration. The objective of this wiki is to explain these main topics and give a better understanding of how hydraulics relates to stream restoration.


 * General Principles of Hydraulics **

Many of the terms and principles used in hydraulics are defined in the more general field of study known and fluid dynamics. For more information about the study of fluid dynamics please follow the link here: [|Fluid Dynamics]. Although many of these principles sound very similar in their definition, they are all different and relate to hydraulics in their own unique way. It is important to understand these principles of fluid dynamics as they are utilized and referenced in stream restoration on a regular basis. Streams undergo many different flow regimes as they undergo many different changes along their length. Various factors such as roughness, slope, and hydraulic structure affect this flow. Therefore, the definitions that explain each one of these cases and are explained below.


 * Uniform, Gradually Varied and Rapidly Varied Flow **

Uniform Flow (UF), in a very basic sense, is flow of a fluid in which each particle moves along its line of flow with constant speed and in which the cross section of each stream tube (or channel) remains unchanged. This typically will only happen in an engineered channel. Uniform flow can be identified by two defining characteristics  . The first is that the average depth flow velocity and area of cross-sections of the flow are constant everywhere along the channel. The second is that the energy grade line, the water surface slope, and the bed slope are all parallel in the channel.   Gradually Varied Flow (GVF) usually occurs when there is a small and gradual change of slope in the channel, as well as small changes in the roughness of the surface over which it. The profile of water in GVF differs from UF in that the fluid particles do not move along the line of flow with constant speed. Rapidly varied flow consists of instances where water is undergoing rapid change in slope of the channel (i.e. water going over a spillway). Rapidly varied flow is often associated with shifts between supercritical and subcritical flow (described below), and vice versa. The particles that move along the lines of flow are changing velocities rapidly.


 * Steady vs. Unsteady Flow **

Steady flow can be easily defined as a flow in which fluid characteristics (velocity, turbulence, pressure, etc.) are not changing over time. Flows that are changing over time are called unsteady flows. This principle can be applied to inherently disordered flows such as turbulent flow if the amount of turbulence over a section that is not changing with respect to time. The principle of steady flow is important because it helps to reduce the amount of inputs into complicated studies of fluid dynamics that multiple inputs.

**Subcritical vs. Supercritical Flow **

Supercritical and Subcritical flow can be defined as two stable conditions with the same energy states within the fluid flow. Supercritical flow is at a higher kinetic energy state in which the fluid is moving faster than the wave velocity. Subcritical flow is defined by a lower kinetic energy state in which the fluid is moving slower than the wave velocity. A simple example demonstrating supercritical and subcritical flow can be seen in Figure 3. The smooth tongue of water pouring over the drop just to the left of the channel center-line is supercritical flow, and the whitewater at the base is the hydraulic jump where flow becomes subcritical again.



<span style="font-family: Arial,sans-serif; font-size: 90%;">The flow regime can be described using a dimensionless term known as the [|Froude number]. The Froude Number represents the ratio of inertial and gravitational forces and, thus, <span style="font-family: Arial,sans-serif; font-size: 90%;"> subcritical flows are defined as numbers below 1 (gravitational forces dominate) and supercritical flows are numbers above 1 (inertial forces dominate). As flows transition from supercritical to subcritical, a [|Hydraulic Jump] occurs and associated energy loss takes place.




 * <span style="font-family: Arial,sans-serif; font-size: 13pt;">Hydraulic Calculations **

<span style="font-family: Arial,sans-serif;">A study of the effect of hydraulics on stream restoration calculations must be made to explain and quantify existing, historical, and future conditions of the fluid in the stream. These calculations quantify various conditions and make it possible for experts in the field to make decisions about what is needed to be done in stream restoration and other areas of research such as water resources engineering. See related: Environmental flows, Physical habitat, Channel evolution model


 * <span style="font-family: Arial,sans-serif;">Manning’s Equation (Normal Depth) **

In the field of Open Channel Flow, Manning's Equation is one of the most commonly used equations. It was invented by an engineer from Ireland in 1889, his name is <span style="font-family: Arial,sans-serif;">Robert Manning. This equation is a variation of the Chezy Equation. It is an empirical equation that applies to uniform flow in open channels and is a function of the channel velocity, flow area, and channel slope.

<span style="font-family: Arial,sans-serif; font-size: 10pt;"> <span style="font-family: Arial,sans-serif; font-size: 10pt;">where:
 * // V // || is the cross-sectional average velocity ( [|L] / [|T] ; ft/s, m/s) ||
 * // k // || is a conversion factor of 1.486 (ft/m)1/3 for [|U.S. customary units], if required ||
 * // n // || is the **Gauckler–Manning coefficient** (T/L1/3; s/m1/3) ||
 * // Rh // || is the hydraulic radius (L; ft, m) ||
 * // S // || is the slope of the water surface or the linear [|hydraulic head] loss (L/L) (//S// = //hf/////L//) ||

<span style="font-family: Arial,sans-serif;">In the field of open channel flow, a great deal of information about the flow can be determined through Manning’s equation - i.e. the relationship between velocity, the roughness coefficient, n ([|more information here]), slope, and hydraulic radius. Manning's equation is an empirical equation that deals with gravity fed free-surface flow. For more information about the [|Manning's Equation can be found here]. An [|Interactive Manning’s Equation Calculator can be found here].

<span style="font-family: Arial,sans-serif;">See related: Channel design


 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Continuity Equation **

<span style="font-family: Arial,sans-serif;">The [|Continuity Equation] <span style="font-family: Arial,sans-serif;"> explains the phenomena of transporting a conserved mass, energy, momentum, ect. For open channel hydraulics, it is used to explain the basic principle of the conservation of mass, energy, and momentum.

<span style="font-family: Calibri,sans-serif; font-size: 11pt;">

<span style="font-family: Arial,sans-serif; font-size: 10pt;">Where <span style="font-family: Arial,sans-serif; font-size: 10pt;">Q = Flow (L3/T) <span style="font-family: Arial,sans-serif; font-size: 10pt;">V = Velocity (L/T) <span style="font-family: Arial,sans-serif; font-size: 10pt;">A = Area (L2)

In stream restoration, the continuity equation can be used heavily. Velocity, which is one of the most important parameters for creating beneficial habitat for plants and animals, can be calculated against proposed channel area modifications. If the channel is constricted in areas, velocity will increase, thereby providing less than optimal habitat and also increasing the potential for scouring of the stream banks. See related: Bank stability, Channel design, Environmental flows


 * <span style="font-family: Arial,sans-serif;">Energy Equation **

<span style="font-family: Arial,sans-serif;">The energy equation used in hydraulics is based on the first law of thermodynamics and can be viewed as an expansion of the Bernoulli Equation. The first law of thermodynamics where “time rate of increase of the total stored energy of the system = net time rate of energy addition by heat transfer into the system + net time rate of energy addition by work transfer into the system.” (Munson p. 223). Or in other words, energy will always be conserved.

<span style="font-family: Calibri,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,sans-serif; font-size: 10pt;">Where: <span style="font-family: Arial,sans-serif; font-size: 10pt;">p/ γ <span style="font-family: Arial,sans-serif; font-size: 10pt;"> = Pressure Head <span style="font-family: Arial,sans-serif; font-size: 10pt;">V2/2g = Velocity Head <span style="font-family: Arial,sans-serif; font-size: 10pt;">z = Elevation Head <span style="font-family: Arial,sans-serif; font-size: 10pt;"> hl = Head Loss <span style="font-family: Arial,sans-serif; font-size: 10pt;">hp = Pump Head

The energy equation is a key underlying equation for solving open channel hydraulics problems and is the foundational relationship within models such as [|HEC-RAS] (details below). The equation is solved using the Standard Step method and the Manning's Equation is used to estimate head loss (energy loss due to friction). See Related: Channel design


 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Momentum Equation **

<span style="font-family: Arial,sans-serif;">The momentum equation used in hydraulics is based on Newtons Second Law, F=ma. Since there are many things going on in fluids that this equation does not directly take into account, a different form is used. The two variables that we need to take a deeper look at are the sum of the forces, F, and also the acceleration of mass (mass is assumed constant, we take this from the continuity equation). Since fluid motion is in three dimensions we need to take into account the x, y, and z direction forces and accelerations.

<span style="font-family: Arial,sans-serif;">A commonly used equation that applies Newton's second law to fluid dynamics and hydraulics is the [|Navier-Stokes] equation. This is used primarily for pipe flow.

Another equation used is the [|St. Venant Equations] when applied to open channels. It is used primarily to route unsteady flows and to investigate force interactions including drag forces on structures.

See Related:Channel design, Environmental flows, Physical habitat


 * <span style="font-family: Arial,sans-serif; font-size: 14pt;">Hydraulic Models **


 * <span style="font-family: Arial,sans-serif;">1D models and assumptions (HEC-RAS) **

<span style="font-family: Arial,sans-serif;">To meet the needs of modern engineering one dimensional hydraulic models such as HEC-RAS were developed to speed up the process of analyzing hydraulic systems and the way that water moves through rivers and channels. 1-D modeling does not take into account the direct hydraulic effect of changes in dimensions to cross-sections, bends and the two or three dimensional aspects of the flow. HEC-RAS was developed to utilize the concepts such as the momentum and energy equation and its variables as well as the Saint-Vernant equation to assess flows in channels. It is able to output information about where hydraulic jumps may exist, if the flow is sub or super critical, flow velocity, discharge, and stage height. For more information about [|HEC-RAS]click the link. See Related: <span style="font-family: Arial,sans-serif;">Sediment transport models, Channel design, Hydrology


 * <span style="font-family: Arial,sans-serif;">2D models and assumptions (SRH-2D, RMA, CCHE2D) **

<span style="font-family: Arial,sans-serif;">Two dimensional models are similar to one dimensional models in many ways but one of the main differences between the two is the ability to model flow outside of the main channel is not flowing parallel to the main channel. The advantage of this ability is that the model is more accurately able to predict flow in situations where flow goes above the main channel into the floodplain. Models that have been developed to deal with 2-D flow are [|SRH-2D], [|RMA], and [|CCHE2D]. See related: Fluvial geomorphology, Sediment transport models


 * <span style="font-family: Arial,sans-serif;">Advantages to using 2-D **

<span style="font-family: Arial,sans-serif; font-size: 12pt;">a) <span style="font-family: Arial,sans-serif;"> The ability to represent irregular boundary configurations <span style="display: block; font-family: Arial,sans-serif; text-align: justify;">b) Variable mesh size, so that extra detail can be applied in areas of special interest. <span style="font-family: Arial,sans-serif; font-size: 12pt;">b) <span style="font-family: Arial,sans-serif;">Direct solution of steady state problems and longer time steps with the implicit solution for dynamic problems. <span style="display: block; font-family: Arial,sans-serif; text-align: justify;">RMA2 is a two dimensional depth averaged finite element hydrodynamic numerical model. It computes water surface elevations and horizontal velocity components for subcritical, free-surface flow in two dimensional flow fields. RMA2 computes a finite element solution of the Reynolds form of the Navier-Stokes equations for turbulent flows. Friction is calculated with the Manning’s or Chezy equation, and eddy viscosity coefficients are used to define turbulence characteristics. Both steady and unsteady state (dynamic) problems can be analyzed.


 * <span style="font-family: Arial,sans-serif;">3D models (Fluent, OpenFOAM, etc) **

<span style="font-family: Arial,sans-serif;">Three dimensional models are very new in the field of hydraulics and their use has been limited cases but has been starting to gain some ground in its application. Finite element programs such as [|Fluent] have started to analize hydraulic problems. Another program that is on the market that has some use as well is [|OpenFoam]. 3-Dimensional models are heavily used in Mechanical Engineering for things such as aerodynamics for vehicles, stresses on materials, and stresses on mechanical parts yet have not been utilized very widely in stream restoration due to the complexities of natural systems. <span style="font-family: Arial,sans-serif; text-align: justify;">See related: <span style="font-family: Arial,sans-serif; text-align: justify;">Sediment transport models


 * <span style="font-family: Arial,sans-serif; font-size: 14pt;">Hydraulics and Stream Restoration **

<span style="font-family: Arial,sans-serif;">The study of hydraulics has many applications in the field of Stream Restoration. Without understanding the hydraulic effect on the physical aspects and habitat of proposed restoration projects, efforts, and funds could be misused or wasted. The following section reviews two scholarly papers that relate the study of hydraulics to rivers and restoration projects.

<span style="font-family: Arial,sans-serif;">See Topics related to "Hydraulics and Stream Restoration" in table after conclusion. =2-D Modeling in Stream Restoration=

<span style="font-family: Arial,sans-serif;">The use of 2-D modeling for rivers has been limited in recent history. It is now being utilized more often, even for water restoration projects. This section will focus on the advantages and disadvantages of 2-D Modeling as well as pointing out flaws of conventional 1-D modeling approaches. Also discussed in this section is a case study done on the North Fork River in California and how 2-D modeling was utilized to assist in restoration efforts. (Crowder and Diplas, 2000)


 * <span style="font-family: Arial,sans-serif;">Disadvantages to 1-D modeling **

<span style="font-family: Arial,sans-serif;">1-D modeling is limited to single depth and single velocity value outputs from the model. This is not always bad and can actually be very useful in determining design specifications for flood management structures but can have limitations when considering more than that. Things that cannot be modeled are velocity gradients and transverse flow, which can have a great impact on the flora and fauna of a stream habitat. Only large scale objects can be modeled and smaller objects in the meso-scale (such as boulders, root wads, ect.) must be accounted for by adjusting a roughness factor.


 * <span style="font-family: Arial,sans-serif;">Advantages to 2-D Modeling **

<span style="font-family: Arial,sans-serif;">2-D modeling has distinct advantages in stream restoration where 1-D modeling is lacking. It accurately and explicitly quantifies spatial variations and combinations of flow patterns. Knowing these variations and combination flows can benefit the flora and fauna of the stream habitat. 2-D modeling can even model the smallest of features where 1-D modeling cannot. This spatial information can provide better habitat metrics for stream restoration projects.


 * <span style="font-family: Arial,sans-serif;">Disadvantages to 2-D Modeling **

<span style="font-family: Arial,sans-serif;">Even though 2-D modeling has many advantages, it is not without its limitations and disadvantages. To have an accurate model, channel geometry must be described exactly. This can be a challenge and, in some cases, even impossible due the dynamic nature of channel geometry. Assumptions must be made about the channel in order to deal with this uncertainty of certain parameters which can greatly affect the results of the model. To deal with this disadvantage, key features must be identified and studied individually as to their effect on system dynamics.


 * <span style="font-family: Arial,sans-serif;">Case Study in using 2-D modeling for Stream Restoration **

<span style="font-family: Arial,sans-serif;">In a case study done on the North Fork of the Feather River in California USA 2-D modeling was used to optimize the placement of single objects on the flow velocities for fish habitat. A mesh for the site was constructed with high and low details. The effect of doing this was to study the difference between a smaller scale (higher resolution) and a larger scale (lower resolution) on the flow velocities. See Figure 1 for a visual representation of this.



Figure 5: Mesh Sizes (Crowder and Diplas, 2000)

<span style="font-family: Arial,sans-serif;">This mesh could then be inputted to the model to analyze the effect of the boulders placed within it. The 2-D model showed that the effect of these boulders was beneficial to the fish habitat because it created low velocity areas in which the fish can spawn and use less energy (see Figure 2).



Figure 6: Results (Crowder and Diplas, 2000)

<span style="font-family: Arial,sans-serif;">Another interesting thing that came out of this study was using the model to place single objects such as boulders in different locations to optimize their effect in creating these low velocity zones. Figure 3 shows the result of doing this using the 2-D model.



Figure 7: - Placement of a Single Object (Crowder and Diplas, 2000)

Impacts of riparian vegetation on hydrological processes
<span style="font-family: Arial,sans-serif;">The impact of riparian vegetation is reviewed and summarized to give a better understanding of the hydrologic interaction of flows in rivers/floodplains and riparian vegetation. This section will be focused on three main influences of riparian vegetation on hydrologic processes based on research done by Tabacchi, 2000. These three main influences include “(i) the control of runoff, i.e. the physical impact of living and dead plants hydraulics, (ii) the impact of plant physiology on water uptake, storage and return to the atmosphere, and (iii) the impact of riparian vegetation functioning on water quality” (Tabacchi, 2000).


 * <span style="font-family: Arial,sans-serif;">Main Channel – regular and low flows **

<span style="font-family: Arial,sans-serif;">The interaction of vegetation can have a great effect on both low flows and high flows or flooding. It has been shown that having a dense amount of “highly patchy” pioneer vegetation such as grassy or herbaceous vegetation can help to trap sediment which aids in water retention time as well as providing a much more stable soil for other vegetation to establish healthy roots in. Pioneer Trees can also have a significant impact on channel hydraulics by establishing sand and gravel bars. Changes or invasions of different species of trees can alter the physical shape and function of rivers due to their ability to trap and store sediments carried by the river. A good case of this is in the Southwest United States where the fast colonizing species Salt Cedar has altered flows in many of the rivers.


 * <span style="font-family: Arial,sans-serif;">Debris types and effects **

<span style="font-family: Arial,sans-serif;">In small streams, the effect of biomass such as litter mats deposited by the riparian canopy can have a great effect on local hydraulics. Little is known about the exact mechanics of this interaction but it has been observed in areas such as forests of middle Garonne (SW France) where there is a great concentration of Willow trees and the biomass deposited by them is great in comparison to other systems (Chauvet, 1989; Chauve and Jean Louis, 1988). Although little qualitative information is known about little wads, the interaction that has been observed as to its effect is that they can create successions of riffles and pools as well as impact pathways within the main channel.

<span style="font-family: Arial,sans-serif;">One type of vegetation debris that is well studied as to its qualitative effect is coarse woody debris (CWD) (Harmon et al., 1986; Maser and Sedell 1994; Gurnell et al., 1995). CWD can cause water to be diverted, disconnect secondary water bodies, and increase local erosion. Although it has been the general practice by river managers to remove the buildup of CWD around hydraulic structures, there have been many studies done that show the positive impacts of CWD. CWD can greatly improve channel stability if allowed to interact with riparian vegetation. CWD can help flows be more evenly distributed during overbank flows as well as help to trap sediments that speed up the stabilization of mid channel bars. Another effect that CWD that is of note is its interaction with low flows in small to medium sizes channels. It has been shown that CWD can increase roughness factors between 7% - 100% (average of 55%).



Figure 8: Hydraulic impact of riparian vegetation (Tabacchi, 2000)


 * <span style="font-family: Arial,sans-serif;">Riparian Zone and secondary channels: **


 * //<span style="font-family: Arial,sans-serif;">Floodplains acting as dissipative structures //**

<span style="font-family: Arial,sans-serif;">Riparian vegetation can serve as dissipative structure to flows due to increased hydraulic roughness and physical interaction, which increases turbidity in flows. Little is still known about the exact qualitative interaction of riparian vegetation on higher, low frequency flows some research has been done to quantify its effect (Darby 1999, Tabcchi 1992, Naot 1996). Vegetation has long been seen by river managers as a risk to channel conveyance and has been treated as such by its removal from most engineered channels. While studies have shown that very densely vegetated riparian zones such as the River Severn in the UK increase the flood height (increased risk of flooding), areas that were not so densely vegetated (30% the vegetation of the River Servern) helped to reduce the flood height. Flood dissipation due to riparian vegetation is most likely a function of the absolute size of the channel and width to depth ratio for a given size. Individual plant species have been studied in order to gain an understanding of their effects on flows based on their physical properties (i.e. stiffness values). It has been shown that riparian zones that are primarily homogenous in plant species have a much lower dissipative effect on a variety of flows than a riparian zone that is highly heterogeneous in its plant species.



Figure 9: Influences of riparian vegetation on turbulence and over-bank flooding. (Tabacchi, 2000)


 * //<span style="font-family: Arial,sans-serif;">Hydraulic connectivity //**

<span style="font-family: Arial,sans-serif;">Due to its natural dynamics, riparian vegetation has a great influence on connectivity of the main channel with secondary channels, oxbow arms, and dead arms. Figure 2 shows that the structure and heterogeneity of riparian zones have a great impact on a river's hydraulic connectivity. Still, little is known about this transverse interaction and storage of water within the streams banks. Related to this topic is Floodplain Connectivity


 * //<span style="font-family: Arial,sans-serif;">Flux between river and riparian zones //**

<span style="font-family: Arial,sans-serif; font-size: 10pt;">Riparian zones can serve as flood pulse (Junk et al, 1989) buffers for high flows in streams. Although this is well known, little work has been done to quantify the effects due to the complexity and diversity of existing systems. In some cases, riparian zones can intensify velocities and increase peak flood pulse waves where as in other cases riparian zones can reduce flow velocities and reduce peak flood pulse waves. Some work has been done to model this complex interaction with the floodplain (Samuels, 1985; Wormleaton, 1986) and has provided good estimations of velocities experienced at the edge of the channel/floodplain boundary through simple turbulence models.


 * <span style="font-family: Arial,sans-serif; font-size: 14pt;">Conclusions **

<span style="font-family: Arial,sans-serif;">Hydraulics is a very important field of study that can benefit people of many backgrounds and aid in application and understanding of the physics and mechanics of water flow. With information and research conducted by many experts in the field, these principles can be applied to many situations. The understanding of hydraulics in stream restoration is key and must be further developed to explain the complex interactions of water with natural physical features of a stream, its connecting floodplains, and watersheds.

Hydraulics In connection with other Topics in Water Restoration
Hydraulics is used commonly in the field of river restoration. Below is a list of related wikis that related with the field of Hydraulics.
 * <span style="color: #222222; font-family: Arial,sans-serif; font-size: 10pt;">Physical habitat - https://riverrestoration.wikispaces.com/Physical+habitat
 * <span style="color: #222222; font-family: Arial,sans-serif; font-size: 10pt;">Sediment transport processes - https://riverrestoration.wikispaces.com/Sediment+transport+processes
 * Sediment transport models - https://riverrestoration.wikispaces.com/Sediment+transport+models
 * <span style="color: #222222; font-family: Arial,sans-serif; font-size: 10pt;">Fluvial geomorphology - https://riverrestoration.wikispaces.com/Fluvial+geomorphology
 * <span style="color: #222222; font-family: Arial,sans-serif; font-size: 10pt;">Floodplain connectivity - https://riverrestoration.wikispaces.com/Floodplain+connectivity
 * <span style="color: #222222; font-family: Arial,sans-serif; font-size: 10pt;">Hydrology - https://riverrestoration.wikispaces.com/Hydrology

=Works Cited=

<span style="font-family: Arial,sans-serif; font-size: 10pt;">-Chauvet E. 1989. Production, ¯ux et deÂcomposition des litieÁres en milieu alluvial. Dynamique et roÃle des hyphomyceÁtes aquatiques dans le processus de deÂcomposition. PhD thesis, UniversiteÂ Paul Sabatier: Toulouse III; 243 pp. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Chauvet E, Jean-Louis AM. 1988. Production de litieÁre de la ripisylve de la Garonne et apport au ¯euve. Acta Oecologia, Oecologia Generalis 9: 265±279. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-D.W. Crowder, P. Diplas, 2000. Using two-dimensional hydrodynamic models at scales of ecological importance. Journal of Hydrology 230 (2000) 172–191 pp. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Darby S. 1999. Eect of riparian vegetation on flow resistance and flood potential. Journal of Hydrological Engineering 125(5): 443±453. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Gurnell AM. 1995. Vegetation along river corridors: hydrogeomorphological interactions. In Changing River Channels, Gurnell AM, Petts GE (eds). Wiley: Chichester, 237±260. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Harmon ME, Franklin JF, Swanson FJ, Sollins P, Gregory SV, Lattin JD, Anderson NH. 1986. Ecology of coarse woody debris in temperate ecosystems. Advances in Ecological Research 5: 133±302. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Junk WJ, Bayley PB, Sparks RE. 1989. The ¯ood pulse concept in river±¯oodplain systems In: Proceedings, International Large River Symposium, Dodge DP (ed.), Can Spec. Publ. Fish. Aquat. Sci., 106: 110±127. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Maser C, Sedell JR. 1994. From the forest to the sea: the ecology of wood in streams, rivers, estuaries and ocean. St. Lucie Press: Delray Beach, Florida, 200 pp. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Munson, Young, Okiishi, Huebsch, 2009. Fundamentals of Fluid Mechanics (6th Edition). United States of America: Don Fowley <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Naot D, Nezu I, Nakagawa H. 1996. Hydrodynamic behaviour of partly vegetated openned channels. Journal of Hydrogical Engineering 122(1): 625±633. <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Tabacchi, Eric and Lambs, Luc and Guilloy, Hélène and Planty-Tabacchi, Anne-Marie and Muller, Etienne and Decamps, Henri ( 2000) Impacts of riparian vegetation on hydrological processes. Hydrological Processes, Vol. 14 (n° 16-17). pp. 29 59-2976. ISSN 0885-6087Crowder <span style="font-family: Arial,sans-serif; font-size: 10pt;">-Tabacchi E. 1992. VariabiliteÂ des peuplements riverains de l'Adour. In¯uence de la dynamique ¯uviale aÁ dieÂrentes eÂchelles d'espace et de temps, PhD thesis, U.P.S.: Toulouse III; 227 pp. <span style="font-family: Arial,sans-serif; font-size: 10pt;">Wormleaton PR. 1986. Some Results of A Preliminary Investigation on Flow in Trapezoidal Main Channel and Floodplain. SERC Flood Channels Working Party.

<span style="font-family: Calibri,sans-serif; font-size: 10pt;"> [] <span style="font-family: Calibri,sans-serif; font-size: 10pt;"> [] <span style="font-family: Calibri,sans-serif; font-size: 10pt;"> []

Resources:

[|NEH-653: Federal Stream Corridor Restoration Handbook]

[|NEH-654: Stream Restoration Design]

//by K. Steinhaus//
<span style="display: block; height: 1px; left: -40px; overflow-x: hidden; overflow-y: hidden; position: absolute; top: -25px; width: 1px;">[|Charles P. Hawkins]a, [|Jeffrey L. Kershner], [|Peter A. Bisson], [|Mason D. Bryant], [|Lynn M. Decker], [|Stanley V. Gregory], [|Dale A. McCullough], [|C. K. Overton], [|Gordon H. Reeves], [|Robert J. Steedman] & [|Michael K. Young]