SHALLOW WATER FLOW OVER NON-UNIFORM VARYING AND NON-VARYING BOTTOM TOPOLOGY

Authors

  • G.C.E. Mbah Department of Mathematics, University of Nigeria, Nsukka
  • S. U. Isienyi Akanu Ibiam Federal Polytechnic, Uwanna- Afikpo, Ebonyi State, Nigeria

Abstract

This study stemmed from the work of Okeke (1985) and Mbah(2008) where they studied the Shallow water wave equations for water depth below the undisturbed sea surface where they assumed the water depth (rough and horizontal) to be constant. We considered this as unrealistic and thus a case where the bottom topography is non-uniform (the depth of the water not constant) and varying is treated here. The depth of the water at all points of the bottom which we call h is defined as: h = h/ + x Cot β, where h/ = water depth at points where there is no non-uniform bottom, x is the points where there is non-uniform and varying bottom, and β is the angle of inclination of the non-uniform varying bottom to the leveled area. The solution to the wave equations for shallow water flow suggests the existence of a single wave elevation which still has a singularity in the profile. This consideration predicts more realistic results as we can see that the nature of the wave and also the velocity of flow is strictly a function of the angle, time and the size of the region that is non-uniform and varying. This is a very important result that must be taken note of in the study of shallow water flow in general and the management of shallow water flow problems, most importantly when the bottom topography is not horizontal or uniform at all or any regions of the flow

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Published

2023-09-26

How to Cite

Mbah, G. ., & Isienyi, S. U. . (2023). SHALLOW WATER FLOW OVER NON-UNIFORM VARYING AND NON-VARYING BOTTOM TOPOLOGY. International Journal of Mathematical Analysis and Modelling, 1(1). Retrieved from https://tnsmb.org/journal/index.php/ijmam/article/view/5