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 . : 3D modelling of free forming meanderin evolution without any initial pertubation

Friedkin 1945

The first scope of this study was to investigate the characteristics of meander bends and their evolution over time. Therefore the numerical results are tested against data from a physical model study performed by Friedkin (1945). In a 40.0 m long tilting flume with a 12.0 m wide effective section filled up with sand of about 0.6 m, an initially straight channel, trapezoidal shaped, with an average width of 0.6 m, a depth of 0.088 m and a slope of 0.009, was exposed to a constant discharge of 8.5 l/s with a water level of 0.05 m. The sand material was fairly homogenous with a grain size distribution of d50 and d90 with 0.2 mm and 0.26 mm, respectively and was used as initial bed material. Friedkin (1945) investigated the pattern evolution of this channel. Lateral movements caused the channel to change from straight to a meandering structure. These experimental data were then used to describe the self forming meander evolution. The second scope of the present study was to investigate the question why the channel starts to erode the river bed and banks respectively. On the origin of the meandering in alluvial streams, several experiments were carried out with resulting theories trying to explain this process. From literature it is well known that alternate bar formation is the initial process yielding to meandering. The result of various investigations (Ackers and Charlton 1970, Ikeda 1984, Jäggi 1984) shows that the alternate bar formation appears to be directly flow induced and therefore it is considered to be the first stage of meander evolution. These characteristic bed forms significantly affect the pattern of flow and the sediment movement in straight channels, because the flow around bars produces a shift in the position of the thalweg from one side to another (Figure 3). With continuing time the amplitude of the thalweg increases, eroding the river banks. This process illustrated in figure 2, leads finally to the well known meander structure. Although the reason for the initiation of meandering in terms of alternate bar formation is well known, the origin of bar formation is uncertain. There are different approaches dealing with this topic as discussed in detail by Rhoads (1991). From his point of view, the most reasonable one follows an approach by Yalin (1977). He sees the existence of alternate bars and dunes as a result of periodic deformations of the vertical and horizontal velocity profiles due to disturbances in the structure of the turbulence. This turbulence structure is characterized by zones of high vorticity production, induced by the existing secundary flow which consists of a pair of helical cells with opposite circulations seperated by the corner bisector. This is supported by the approach of Einstein and Shen (1964). Their theory sees the oscillating motion of helical flow as the origin of alternate bar formation. These cells are capable to move sediments in lateral direction in order to create an oscillating thalweg in a straight channel, which induces then the beginning of meandering.

Figure 1: click to see the whole meander evolution over time [animated gif]; [avi format (3.0MB)]

To model a self forming, meandering channel, the CFD program was initalised with the same in-put data as used in the physical model study carried out by Friedkin (1945). In Figure 1 the plan view of the calculated flow pattern over time is illustrated. After 50000 seconds, the figure illus-trates that the formation of bars had developed over the whole channel length and the flow had started to erode the river banks in the most upstream river part of the channel. It can be observed that after a time of 100000 seconds the turbulent secondary currents and the helical flow move-ment had destabilized the cross sections over the whole channel length, starting to develop a me-andering thalweg. After 250000 seconds the simulation stopped and a meander pattern with three wavelengths was developed. It is rather difficult to quantify characteristic dimensions of the me-ander bends, because their length and width increases with the downstream distance. Neverthe-less, the predicted pattern matches fairly well to the observation of the experiments. After 10 m the meander starts to develop ending up with a fully developed meander bend in the most down-stream part of the flume. The numerical investigation also showed, that the meander pattern tended to develop much slower compared to simulations where the inflow conditions contains perturbation elements, like initial bends or skewed inflows (Olsen 2003).

Developement of alternate bars in flume channel of Ackers and Charlton (1970)

Figure 4 shows the river bed evolution after 40000 seconds. It illustrates the contour plot of the calculated bed changes from minus 3.5 up to 3.5cm, and it can bee seen that the formation of al-ternate bars was fully developed. The pattern shows a good agreement to the results of laboratory experiments. The sketched bar pattern of e.g. Ikeda (1984) (Figure 3) exibits the same character-istics as were developed in the numerical model. The river bed is dominated by the oscillating changes in terms of pools and sediment deposition. The pools, sometimes called scour are spread out in the longitudinal direction and are located at the outer region of the channel near the banks (Figure 4a). As already mentioned, the pools are in an alternate formation so that the main water flow is forced to change the sides periodically. This causes accelerations of the masses in the flow and leads to changes in lateral direction over time. It is well known that the wavelength of alternate bars is somewhat proportional to the channel width. In literature there are several ap-proaches suggesting a ratio between these characteristic lengths. Unfortunately they are all differ-ent and not resulting in the same prediction. Fujita (1980) suggested in his thesis to use a propor-tional factor between 3 and 13, defining a fairly wide range. From figure 4b it can be seen that the results out of the numerical model are fitting in this range. The wavelength of the thalweg is equal to four times the channel width. At this time step the cross section are already in a stadium where the channel bank are destabilized by the oscillating flow. The meandering evolution starts to develop.

Figure 3: Alternate bar formation; sketch of bed changes and the developing thalweg. (Ikeda 1984)

(a) Alternate bar formation after 40000 sec. Contour plot of the numerical results of the bed changes; scale: -0.035m to 0.035m
(b) Flow direction of the thalweg

click to see the evolution of the vertical velocities over time [evolution over time]
Figure 5 shows an enlargement of the most downstream bend after 250000 seconds, plotting the contour plot of the water depth. The scale is changed to 0.025 m up to 0.05 m. The figure shows a typical flow situation for the transition zone between two meander bends, which has been ob-served in several investigations. The water depth is greater in the bends than in the other part of the channel. The river bed is narrow and compressed into the bend yielding to steep gradients of the river banks. When entering the transition zone between to bends the flow has space to spread out. Consequently the water velocities decrease and the particles tend to deposit. In this part of the channel the bed has the tendency to develop so-called riffles due to the shallow water depth. Afterwards the flow is entering the following bend to be accelerated by the pressure gradients. The flow velocity in the most outer region increases causing an increasing erosion rate in this area. As figure 5 shows, the computed results of this characteristic behavior shows agreements with the observation from the laboratory experiments.

Flow stucture in a river bend, contour plot of the water depth
A CFD model has been used to simulate a self forming meander pattern over time. From an ini-tially straight alluvial channel, the model computes the lateral motion of the meander bends as well as their movement in longitudinal direction. Hence, the program predicts the process of ero-sion and sedimentation in good agreement with results of the physical model study. This process is a result of a special hydraulic regime in a meandering river system. It is strongly dominated by turbulent secondary currents and helical flow leading to meander development. These phenomena are fairly well reproduced by the numerical model predicting the self formed meander evolution. One aspect of further research is the question of the stability of the river bed development as a whole system. Experiments have shown that sediment feed at the entrance of the flume has a strong impact on the stability of the cross section and consequently of the meander development.

 : . 3D modelling of free forming meanderin evolution without any initial pertubation

 © by NR  Last Update 29.09.2004