Solutions of Navier-Stokes Equation with Coriolis Force

We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimension...

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Published in:Advances in mathematical physics 2017-01, Vol.2017 (2017), p.1-9
Main Authors: Lee, Sunggeun, Lim, Hankwon, Ryi, Shin-Kun
Format: Article
Language:English
Subjects:
Accretion disks
Chemical engineering
Coriolis effect
Coriolis force
Fluid dynamics
Fluid flow
Fluid mechanics
Fluids
Navier-Stokes equations
Nonlinear differential equations
Nonlinear equations
Partial differential equations
Physics
Potential flow
Reynolds number
Steady state
Stokes law (fluid mechanics)
Two dimensional flow
Vortices
Vorticity
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description We investigate the Navier-Stokes equation in the presence of Coriolis force in this article. First, the vortex equation with the Coriolis effect is discussed. It turns out that the vorticity can be generated due to a rotation coming from the Coriolis effect, Ω. In both steady state and two-dimensional flow, the vorticity vector ω gets shifted by the amount of -2Ω. Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow v→=∇→ϕ, the equation satisfied by ϕ is independent of Ω. The remaining Navier-Stokes equation reduces to the nonlinear partial differential equations with respect to the velocity and the corresponding exact solution is obtained. Finally, the steady convective diffusion equation is considered for the concentration c and can be solved with the help of Navier-Stokes equation for two-dimensional potential flow. The convective diffusion equation can be solved in three dimensions with a simple choice of c.
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subjects Accretion disks
Chemical engineering
Coriolis effect
Coriolis force
Fluid dynamics
Fluid flow
Fluid mechanics
Fluids
Navier-Stokes equations
Nonlinear differential equations
Nonlinear equations
Partial differential equations
Physics
Potential flow
Reynolds number
Steady state
Stokes law (fluid mechanics)
Two dimensional flow
Vortices
Vorticity
title Solutions of Navier-Stokes Equation with Coriolis Force
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