A Numerical Expedition through the Mathematical Representation of Complex Braided Morphometry—A Case Study of Brahmaputra River in India

Abstract

The present work explores the process of mathematical representation for the complex geometry of a wide alluvial river with high braiding intensities. It primarily focuses on an approach to developing a numerical solution algorithm for representing the complex channel geometry of the braided Brahmaputra River. Traditional elliptic PDEs with boundary-fitted coordinate transformation were deployed, converting the non-uniform physical plane into a transformed uniform orthogonal computational plane. This study was conducted for the river channel reach with upstream and downstream nodes at Pandu and Jogighopa (reach length ~100 km), respectively, within the Assam flood plain in India, with fourteen measured river cross-sections for the year of 1997. The geo-referenced image covering the river stretch in 1997 was delineated using a ArcGIS software 9.0 tool by digitizing the bank lines. Stream bed interpolation was conducted by interpolating bed elevation from a bathymetrical database onto code-generated mesh nodes. Discretization of the domain was performed through the developed computer code, and the bed-level matrix was generated by the IDW method as well as the MATLAB tool using the nearest neighborhood technique. A mathematical representation of a digital terrain model was thus developed. This generated model was employed as a geometrical data input to simulate secondary flow utilizing 2D depth-averaged equations with the flow dispersion stress tensor as an extra source component, coming from curvilinear flow patterns caused by severe river braiding. The developed model may further be useful in mathematically representing the geometrical complexities of braided rivers with a relatively realistic assessment of the various parameters involved if deployed with improved river modeling with morphometric evolution.