Mathematical modelling of flood Wave: a case study of Budalang'i Flood plain basin in Busia county, Kenya

Abstract

Flooding is a worldwide problem with more adverse e ects in developing countries. In Kenya, severe ooding is experienced on the lower tributaries of Lake Victoria, mainly Budalang'i area. This is indicated in the historical oods of 2003, 2007, 2017 and 2019, leading to mass displacement of people and property destruction. This has attracted attention of researchers worldwide and application of di erent measures to curb ood in the study regions. Mathematical modeling of ood wave has however not been adopted in Budalang'i ood plain. Therefore this study formulated, analyzed and simulated the 2D ood wave model with incorporation of a sink to the Budalangi ood plain. Formulation was applied on existing Navier Stokes equations with the addition of a sink term on continuity equation. Analy- sis of the shallow water model entailed transforming the equations using Jacobian transformation and assessing the nature of ow using Froude number. For simula- tions of the 2D shallow water model, the study adopted a nite di erence scheme to make approximations which solved the system of equations and displayed in the gures . It is realized that in the formulation of the 2D shallow equations, appro- priate model for Budalang'i ood plain is easily derived from the 3D Navier Stokes equations under ood plain assumptions and addition of a sink term is necessary for modelling in the ood plain. Assessment of the properties reveals that super- critical ows are dominant. Addition of a sink term ensures steady state velocity thus reducing higher frequency and turbulence as well as over bank ows while incorporating coriolis term has signi cant e ect on the turbulence. The study concludes that addition of a sink term to the 2D shallow water model will enable control of the oods in the area of study. The ndings will aide disaster manage- ment stakeholder to come up with a more reliable ood prevention technique and new knowledge on how source terms can help reduce ood risk.