A Mathematical Model of Stratified Geophysical Fluid Flows Over Variable Bottom Topography

Iornumbe, S.I.¹, Tivde T.²; and Chia, R.A.¹

¹ Department of Mathematics and Computer Science Benue State University, Makurdi

²Federal University of Agriculture, Makurdi, Benue State.

Corresponding author: iorsteve@yahoo.com.

Abstract

In this paper, a mathematical model of stratified geophysical fluid flow over variable bottom topography was derived for shallow water. The equations are derived from the principles of conservation of mass and conservation of momentum. The force acting on the fluid is gravity, represented by the gravitational constant. A system of six nonlinear partial differential equations was obtained as the model equations. The solutions of these models were obtained using perturbation method. The presence of the coriolis force in the shallow water equations were shown as the causes of the deflection of fluid parcels in the direction of wave motion and causes gravity waves to disperse. As water depth decreases due to varied bottom topography, the wave amplitude were shown to increase while the wavelength and wave speed decreases resulting in overturning of the wave. The results are presented graphically.

Keywords: Bottom topography, coriolis force, geophysical fluid, series solution, shallow water equations, stratification.