TR(BR)-8/97-98 : One dimensional modelling of branched free surface flow

Abstract

Occurrence of branched flow situation is quite common. Flow diversion is one of the techniques used to reduce flooding of a downstream city. This flow may rejoin the stream taking a circuitry route. Sometime, river length is reduced by means of cut-off channel as an channel improvement scheme. The diverted flow may take lower velocity than the main. On the other hand the flow in the cut-off diversion and rejoining at a down stream point. Flow computations in such situations need special attention as the computed flow depths need to satisfy certain conditions at the junctions. Therefore a mathematical model capable of computing the flow depth and the discharge in each of the branched is developed using gradually varied flow equations. The model is the first step towards modelling complex situations like one encounters in braided river.

This model can handle three flow situations viz. (I) temporary flow diversion; (ii) a cut off channel and (iii) a single river island. Computational capability of the model is increased to handle irregular cross sections of a river. Parametric studies have been carried out using this model in order to find out the effect of the diversion channel width on the discharge it can carry for different values of bed roughness and bed slope. A relationship is established between the divided flow, width, slope and roughness coefficient in a dimensionless form for each of the flow situation using least square methods. These equations are derived for rectangular channel. However it is found that approximation to irregular geometry can be applied and the derived equations can be employed with confidence.

The model development and the results discussed in this report are for relatively simpler cases compared to the flow situations normally encountered.