Mathematical modeling 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 effects in developing countries. In Kenya, severe flooding is experienced on the lower tributaries of Lake Victoria, mainly Budalang’i area. This is indicated in the historical floods 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 different measures to curb flood in the study regions. Mathematical modeling of flood wave has however not been adopted in Budalang’i flood plain. Therefore this study formulated, analyzed and simulated the 2D flood wave model with incorporation of a sink to the Budalangi flood 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 flow using Froude number. For simula tions of the 2D shallow water model, the study adopted a finite difference scheme to make approximations which solved the system of equations and displayed in the figures . It is realized that in the formulation of the 2D shallow equations, appro priate model for Budalang’i flood plain is easily derived from the 3D Navier Stokes equations under flood plain assumptions and addition of a sink term is necessary for modelling in the flood plain. Assessment of the properties reveals that super critical flows are dominant. Addition of a sink term ensures steady state velocity thus reducing higher frequency and turbulence as well as over bank flows while incorporating coriolis term has significant effect on the turbulence. The study concludes that addition of a sink term to the 2D shallow water model will enable control of the floods in the area of study. The findings will aide disaster manage ment stakeholder to come up with a more reliable flood prevention technique and new knowledge on how source terms can help reduce flood risk.