| dc.description.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. | en_US |
