Mathematical Model of Geophysical Fluid Flow over Variable Bottom Topography

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.

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Lie symmetries of two-dimensional shallow water equations with variable bottom topography

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/5.0007274 ◽

2020 ◽

Vol 30 (7) ◽

pp. 073132

Author(s):

Alexander Bihlo ◽

Nataliia Poltavets ◽

Roman O. Popovych

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Bottom Topography ◽

Lie Symmetries ◽

Two Dimensional ◽

Variable Bottom

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

NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES ◽

10.46912/napas.202 ◽

2020 ◽

Vol 3 (3b) ◽

pp. 112-137

Author(s):

SI Iornumbe ◽

T Tivde ◽

RA Chia

Keyword(s):

Mathematical Model ◽

Shallow Water ◽

Wave Motion ◽

Wave Speed ◽

Bottom Topography ◽

Nonlinear Partial Differential Equations ◽

Fluid Flows ◽

Variable Bottom ◽

Conservation Of Momentum ◽

Model Equations

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.

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Lie Symmetries and Exact Solutions of Shallow Water Equations with Variable Bottom

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2015-0093 ◽

2015 ◽

Vol 16 (7-8) ◽

pp. 337-342 ◽

Cited By ~ 3

Author(s):

Manoj Pandey

Keyword(s):

Exact Solutions ◽

Shallow Water ◽

Shallow Water Equations ◽

Lie Symmetries ◽

Inclined Plane ◽

Particular Solutions ◽

Governing System ◽

Variable Bottom ◽

Nonlinear Shallow Water Equations

AbstractIn the present paper, Lie symmetries of nonlinear shallow water equations with variable shapes of the bottom that include horizontal, inclined plane and a parabolic bottom are obtained. Exact particular solutions of the governing system are then obtained using the invariance of the system under these symmetries using Lie’s method. The evolutionary behaviour of the $${C^1}$$ discontinuity wave, influenced by the amplitude of the discontinuity wave and the geometry of the bottom, is discussed in detail and some contrasting observations are made.

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