Mathematical Model of Geophysical Fluid Flow over Variable Bottom Topography

Abstract

In this paper, the bottom topography of a geophysical fluid flow is modelled in the presence of Coriolis force by the nonlinear shallow water equations. These equations, which are a system of three partial differential equations in two space dimensions, are solved using the perturbation method. The Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and different kind of flow patterns possible in geophysical fluid flow have been studied and the results illustrated graphically.

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

“…According to Iornumbe et al (2020); the momentum and Continuity equation for the two-dimensional shallow water flow model taking into account the effects of topography and the Earth's rotation was described as below:…”

“…The shortcoming of the model is that it does not take into account the density stratification which is present in the geophysical flow. Iornumbe et al,(2020) considered the model of the bottom topography of a geophysical fluid flow in the presence of Coriolis force, without stratification and a system of three nonlinear partial differential equations in two dimensions was modelled and solved using the perturbation method. Since stratified fluids are very present in nature, present in almost any heterogeneous fluid body, therefore, we considered it in this paper.…”

“…In this paper, a mathematical model for the stratified geophysical fluid flow over variable bottom topography is derived taken into account the density stratification which is present in the geophysical flow and is an extension of the work of Iornumbe et al (2020).…”