The basic form sediments which occur in alluvial channel flow rate related to the flow regime. Flow regime, which is a form that affects the flow of the layer configuration. The following classification shows the relationship between flow velocity and sediment transport modes (sediment transport), the concentration of the transported sediment and forms the basis of the relationship between phase and water (surface water).
Flow regime can be related to the Froude number characterizes whether flow will be calm or fast. Froude number is an expression of the ratio between the inertia (the force needed to stop the moving particles) and gravity.
In general, the basic shape of the flow regime, sediment is classified into: A. Regime low flow B. Regime transition flow C. Regime high flow
A. Regime Low Flow
(Froude number <0.4 to 1 with ramps transition)1. Flat bed, is a sediment transport without deformation and the
movement details are tossing and turning. And the magnitude of the shear of stress is exactly above from the critical.
2. Ripples, the size is <0.6 mm and the shear of stress is become smaller than before. Sediments which has an regular shaped waves with wavelengths of 5-10 cm and a height of 1 cm (base shaped like a regular wave amplitude is relatively small compared with the wavelength).
3. Dunes, all sizes of sediment and the shear of stress increases to the front side. The front side is slope slightly, the back side is steeper. Erosion can occur on all sides of the upper reaches, and deposition occurs at the bottom of the downstream side.
4. Dunes, all sizes of sediment and the shear of stress increases to the front side. The front side is slope slightly, the back side is steeper. Erosion can occur on all sides of the upper reaches, and deposition occurs at the bottom of the downstream side.
B. Regime transition flow(basic configuration of the dunes towards the plane bed or anti-dunes)
C. Regime high flow(Froude Number> 0.4 to 1, a relatively small flow resistance and large sediment’s transport)
1. Plane bed, Plane bed, has a flow rate gradually rising, sediment transport has a flat height. The movement of the Grain is rolling or sliding and changes at a particular place. A fine material occurs saltasi.
2. Antidunes, has sediment materials occurs in the upstream dunes, erosion on downstream. More or less symmetrical waveforms. Antidunes move downstream and occurs at Fr> 1
3. Chute and Pools, occurs in the slope, velocity and sediment discharge which are relatively large. The basic form is a hill - a large sediment hill. The state of the flow in chute is supercritical or subcritical.
I. Bedform Forecast
Determining the criteria of bedform, approach used by the sediment continuity equation as follows:
s + = 0
description:s = specific weight of bed material y = height of bedform at x along the river t = time qs = sediment flow in a weight unity wide and time
The first limitation showed a decrease in the rate of sediment at the base, and the second limit sediment transport shows the change in the change of the
distance x along the river. It turns out that both these limits gradually always
opposite in sign, when the base is formed positive and negative.
.
The image above shows the cross-sectional shape at time t and t + dt from the bedform that moves downstream. In the upper part of the lower forms of the
basic situation which is a function of time, so negative.
From this equation, seemingly that positive, so that qs increases
continuously until it reaches its peak.
Exner (1925), assumed that: qs = Ao. uo
Ao = constant Uo = flow velocity near the base
By entering Ao and Uo into the sediment Equalition continuity before, then obtained :
s + Ao = 0
In 1963, Kennedy introduced the relation between the wavelength L of a change in the bedform of the Froude number
Results of Kennedy’s investigationed to the dominant wavelength of the form - the bedform is:
Fr2 = =
Specification: Fr = Froude number d = depth of flow U = velocity of flow k = 2π / L = wave number L = wavelength j = ᵟ / d = deceleration factor ᵟ = distance which can lead to changes in local sediment flow deceleration and change of pace near the base The concept of "lag distance" was first proposed by Kennedy (1963) and is the most important factor.
Pictured above is the theoretical curve obtained kennedy with entering data into the equation the dominant wavelength (the relationship between Fr and kd).
Seen in Fr2, greater than (1 / kd) tanh kd, and the kd <2
Curve Fr2 = (1 / kd) tanh kd give upper limit for ripples and dunes Fr. Transition area between Fr = 1 and Fr = 0.844
Kennedy proposed a simple relationship between the wavelength L antidunes with average speed U as follows:
U2 = This equation is known as the equation for the wave speed in
the water.
From experiments K/ennedy (1963) obtained results that were passed antidunes surface waves break when the position is steep. Comparison between wave height to wavelength is between 0.13 and 0.16 and between the retrieved value is 0.14 for the water wave steepness at the time began to break.
II. Kekasaran alluvial
In an alluvial channel, the various regimes of bed forms are the results of complicated interactions between the overlying flow and the mobile bed sediments. The physics of bed form is complicated because the flow boundary is not fixed but changes dynamically according to the sediment characteristics, channel shape and flow strength, among other factors. The variable bed forms modify the flow resistance and therefore the stage-discharge relationship of the channel conveyance. The mobile bed resistance depends on many interrelated factors including the skin or grain resistance and form drag or bed form resistance. The former is dependent on the depth of flow and grain size at the boundary surface while the latter is the resistance associated with the eddy formations and secondary circulations set up by the flow over the bed form. Whereas the flow resistance for a given flow depth and velocity in a rigid boundary channel is approximately constant with time, it is not so for a mobile bed channel with bed forms. The flow resistance in the latter needs to consider the contribution of both the grain and bed form resistance. Generally, the equation for total shear stress acting on a sand bed is given by:
τ0=ρgRS _______________________(equation 1)
ρ= fluid density
g= gravitational acceleration
R= hydraulic radius related to bed
S= energy slope
The current practice is to treat the total bed shear stress as the sum of two shear stress components corresponding to the grain and bed form resistance, which is:
τ 0= τ 0+ τ 0*_______________________(equation 2)
1. Einstein-Barbarossa (1952) Divide hydraulic roughness to 2 parts: R’ and R’’
Which is R=R’+R’’
U*’ (Shear velocity related to grain size), calculated with ks (correction factor), in this relathionship with Chezy method: U/U*’=5,57log[12,27(R’/ks)x]
Einstein-Barbarossa Graphic
2. Engelund-Hansen (1976)
They assumed a constant pgR on both sides of equation (2) andintroduced an alternative approach based on the direct summation of two energy slopes. Equation (2) becomes:
S=S’+S”
Where: S’ is the energy slope due to grain resistance and S” is the component due to the bed form resistance. The argument is that the additional energy loss
associated with S” is the result of the ‘‘sudden expansion’’ of flow at the lee side of the bed forms.
Moreover, Engelund and Hansen make the f(function of bed form steepness):
f = f’+f”
f = f’+(αH2)(hL)
Engelund-Hansen Graphic
3. Lovera-Kennedy (1969), Alam-Kennedy (1969)Restrictions for Lovera-Kennedy dan Alam-Kennedy:a. Base sediment characteristic =D50
b. Limited analysis for gravel and waterc. Gravity reaction=0 and there is no free surface waves
The analysis result is: λ’=f(Re=(U.R)/v.R/D50)v= kinematic viscosity of fluidR= hydraulic radiusλ’=friction factor Darcy Weisbach
