2-D DEPTH AVERAGED MODELLING FOR CURVILINEAR BRAIDED STRETCH OF BRAHMAPUTRA RIVER

Abstract

The Brahmaputra is the largest river in the Indian subcontinent and ranks fifth in the world in terms of discharge. The specific yield from its catchment area is one of the highest in the world due to incidence of very high rainfall on a narrow drainage basin. Significant areas of prime inhabited land are lost every year to river erosion in the Brahmaputra basin. Furthermore, unrelenting bank erosion process has caused channel braiding which created navigation bottle-neck zones in the Brahmaputra due to inadequate draught during non-monsoon. For efficient management of prevailing problem spanning over hundreds of kilometre length along the Brahmaputra, the need has arisen for a convenient scientific methodology which can aid systematic monitoring of braiding behaviour, help prioritization of erosion zones, and maintain navigational all-weather fairway. River morphological processes are among the most complex and least understood phenomena in nature. Hence for addressing numerous related hydraulic engineering problems, understanding flows through open channels, is of crucial importance. These flows are typically turbulent and highly three- dimensional. Traditional approaches for studying natural river flows and morpho-dynamics study are based on field measurements and laboratory experiments. Owing to site and event specific concerns, field studies of natural open channel flows are very expensive, tedious and time consuming. Similar problems are associated with laboratory physical model studies, which suffer from scale effects owing to non- similarity of one or more dominant non dimensional parameters. To overcome above shortcomings, developments of numerical models that generally do not exhibit aforementioned difficulties are being stressed upon. The geometric complexities induce very intricate three dimensional turbulent shear flows which are characterized by secondary currents, vortex formation, flow reversal, and anisotropy effects. Majority of existing numerical models have focused primarily on the study of rivers of simplified geometries. The initial attempts in application of mathematical models in conjunction with empirical functions obtained from laboratory experiments to the investigation of morphological processes can be found in the 1950s. Research in this direction was intensified and broadened in the 1970s and later. However 3-D numerical models are yet to be fully and adequately developed for channel with complex geometry in macro scale river reaches. Solving the equations of motion in these conditions is very difficult and computationally tedious. In rivers where the width of the flow is large compared to its depth, the vertical acceleration of water is negligible compared to the gravitational acceleration. In this condition, the pressure distribution in depth can be assumed to be hydrostatic. Hence, in order to ease the numerical complexity and without compromising much with the results, the equations of motion can be integrated in depth to derive two-dimensional depth averaged equations. Wherever the channel domain becomes curvilinear in nature, either well defined meanders, braiding, curved bank-lines or 3-D flow structures are bound to develop on account of dominant secondary flows. The secondary flow is transverse circulation induced by centrifugal forces. Incorporating adequately the effect of secondary flow further enhances the two dimensional modelling to assess the realistic flow field. Thus, with less expensive numerical effort, a better and improved flow scenario can be achieved without going into 3-D model development. Problem identification The Assam section of the Brahmaputra River is in fact, highly braided and characterized by the presence of numerous lateral as well as mid channel bars and islands (Goswami and Das, 2000). Due to these facts, the research on Brahmaputra River in the past mostly relied on field investigation and physical modelling. Only after 1980s, numerical modelling, especially 1-D modelling has been gradually applied in flow simulation and sediment prediction in Brahmaputra River (Sharma, 2004). Yet successful implementation of 2-D depth averaged modelling in Brahmaputra River reaches in Assam Flood Plains is hardly found in literature due to its highly complex topography and difficulty in reproduction of geometric data mathematically. A number of investigations have been done so far to develop numerical models to represent the processes involved in braided river. Correct process representation of the river vi morphology is yet to be achieved by improving fluvial features like impact of secondary flow due to channel bends on the flow field. With this background, development of an enhanced 2-D depth averaged numerical model and its application in identified reach of Brahmaputra River is attempted to critically analyse the effect of flow features for better understanding of braided river behaviour. Objective of the study The first objective of proposed research work was set with the application of principles and practices of numerical model development, to derive the appropriate set of mathematical expressions for the secondary flow correction (flow dispersion stress tensor) for depth averaged 2-D model to be used for non-orthogonal curvilinear flow domain. The second objective was to develop numerical algorithm using finite volume method to solve conservative form of governing equations in non-orthogonal grids with incorporated flow dispersion stress terms in momentum equations and compare' the results of flow model with and without flow dispersion for general curved channels. The 41; third objective was to apply and verify the proposed numerical model for the Brahmaputra River in selected reach and possible identification of braiding pattern with variability in stage-discharge. The fourth objective was to evolve a simplified braiding indicator to express the measure of braiding intensity for a river reach with incorporated no flow zone within the flow domain. The study area and data collected The reach between measured cross sections number-22 (Pandu near Guwahati) to 9 (Jogighopa) released by Brahmaputra Board, .G.0.1. (spanning over approx. 100 km length in Assam state of Indian Territory) is selected for this study. Fourteen measured river cross-section data (Cross-section no. 22 to Cross section no. 9) for the year 1997 were used. Discharge data of the river Brahmaputra during 1997 was used in the study (Central Water Commission and Brahmaputra Board, G.0.1.). The digital satellite data comprising scenes of Indian Remote Sensing (IRS) Linear Imaging Self Scanner (LISS-III) sensors for the year 1997 (Unpublished report of National Disaster Management Authority, Govt. of India) for the study area, have been used. For model verification and vii evaluation, an experimental flume of test section (4.25mx0.15mx0.20m) comprised a contraction in between with 0.002 m3/s of constant discharge was simulated. Methodology The boundary fitted coordinate system has been used to describe a naturally shaped boundary to represent the complex flow domain. The e=-axis is drawn along the channel for a given channel shape and 1- axis is set to intersect the caxis, Then the plane 1) is divided into the structured cells to form the mesh for computations using Poisson's equation. The governing equations for estimating flow field are transformed from Cartesian co-ordinate system to a Boundary fitted curvilinear co-ordinate system to represent flow domain. Finite Volume Method conserves mass-momentum and can be well applied for highly complex geometry using non-orthogonal grids. The flow field is computed at geometric cell centers using the Finite Volume Method using SIMPLEC algorithm. Rhie and Chow's (1983) interpolation technique is used to estimate the velocities at cell faces. The flow field and water depth are computed using the derived transformed governing equations with special attention to boundary implementation. The river braiding is simulated with incorporation of wetting and drying technique into the numerical solver. A C++ computer code has been developed for numerical model to simulate flow field and mesh generation. Proposed governing equations The governing equations for flow simulation are RANS (Reynolds Averaged Navier Stokes) equations with depth averaged approximation of continuity and momentum equation in generalized curvilinear coordinate system. Components of dispersion stress terms are included in momentum transport equations as additional source/sink term. The derivation of dispersion stress tensor is done step by step to get revised set of empirical relations to be used in subsequent development of enhanced 2-D numerical flow model. The derived expressions are modifications to earlier relevant investigations (Duan, 2004; Duan and Julien, 2005). The proposed formulations are with simplified mathematical representation and are numerically compatible. These also improved the flowfield simulation reasonably. viii Validation of the developed 2-D model and salient contribution of the present research work 1-D flow models are insufficient to tackle problems of braided streams due to lack of information with regard to transverse flow field. So, 2-D or 3-D models are used. 3-D models are numerically expensive for macro scale river reaches. Hence, 2-D enhanced 54 model was developed. Most of the 2-D models developed especially for braiding rivers did not account for secondary flow correction probably presuming these corrections to be insignificant for turbulent flows and mild curved bank-lines. But in complex flow situation with considerable braiding, the secondary flow correction is suitably justified to achieve improved flow scenario with nominal additional expense in respect to computational effort with including secondary flow correction using modified terms for dispersion stress tensor in the flow momentum equations. Developed model was initially verified with flume experiment operating a flow with a contraction, and the validation of the flow simulation was achieved. It is established from the model application in laboratory flume that redistribution of flow concentration in longitudinal and transverse directions are desirably accounted for, using the formulation in curvilinear flow field and are well capable of assessing realistic flow prediction with reasonable approximation. The model developed in this study has been applied and verified in the selected stretch of Brahmaputra River. It was observed that the effect of dispersion stress tensor in flow field increases with increase in braiding intensity. The model results lend support to this observation. When braiding intensity increases, it evolves multiple channels with meandering configurations within the domain of stream flow. Meandering and bend in evolved multiple channels instigate more discrepancy in the flow-field, if it is approximated with depth averaging. Braiding induces severe bank erosion, due to dominant transverse flow field. So, improved and realistic flow-field estimation will lead to realistic assessment of predictions of bank erosion and river bed evolution for braided alluvial rivers. Better erosion models can be developed with reasonable accuracy using estimated flow field as the prime input. ix Based on the obtained results and information from flow simulation for twenty discharge profiles at receding flood of 1997 for Brahmaputra River stretch under this study, an indicator namely braid power is proposed based on the model output to express the measure of braiding for a river reach as YanterS braid powe r (N/mz - s) = fn.( flow Area of Inlet of the Reach where, ic,f =Ratio of no flow zone area with respect to whole flow domain area, rUnit weight of water (N/m3) and S=Average longitudinal slope of the study reach. Flow area (m2) is the cross-sectional flow area of the inlet boundary at the given discharge. It was observed that braid power increases with decrease in incoming discharge into the reach at a particular instance of time. The rate of decrease or increase of braid power depends upon geometric configuration of the reach at the particular instance of time along with other factors Scope for future work and limitations The numerical model developed in this research work is limited to flow field simulation in rivers with highly complex geometries and braided configurations. The prime thrust of the present research work is to bring to the fore persistent shortcomings in relation to flow field estimation for rivers with highly braided configuration. The present research work has desirably brought about a significant improvement in dominant transverse flow field estimation in highly braided rivers. The transverse flow field is one of the significant causative factors for stream bank erosion resulting in huge land loss around the vicinity of braided rivers such as Brahmaputra River. However, to model bank erosion and bed evolution with high degree of accuracy, after further research, a robust 2-D sediment transport module with incorporated bank erosion mechanism, clubbed with the present enhanced flow simulation model is required to be developed. To model the moving boundaries, present developed model uses fixed boundary method through implementation of wetting and drying technique including the whole flood plain under the flow domain. However through conducting further research on advanced algorithm using depth adaptive grid generation and temporal deformed mesh technique; a moving boundary can possibly be implemented to simulate the multiple channels actual flow zones instead of considering the whole flood plain. However, at present numerical implementation of the aforesaid process is quite complex for highly braided rivers with multiple channels like Brahmaputra and possibly be a potential area of research. **************************************** xi