Solutions of Navier-Stokes equation with Coriolis force
type: Item
instance of: scholarly article
title: Solutions of Navier-Stokes equation with Coriolis force
zbMATH Open document ID: 1448.76062
DOI: 10.1155/2017/7042686
author: Sunggeun Lee
author: Shin-Kun Ryi
author: Hankwon Lim
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: 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, \(\Omega\). In both steady state and two-dimensional flow, the vorticity vector \(\omega\) gets shifted by the amount of \(- 2 \Omega\). Second, we consider the specific expression of the velocity vector of the Navier-Stokes equation in two dimensions. For the two-dimensional potential flow \(\overset{\rightarrow} {v} = \overset{\rightarrow} {\nabla} \phi\), the equation satisfied by \(\phi\) is independent of \(\Omega\). 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 \(c\).
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 6962660
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/7042686
OpenAlex ID: W2747176103
cites work: Vortex Dynamics
cites work: Exact solutions of the Navier–Stokes equations having steady vortex structures
cites work: Laplace's equation for convective scalar transport in potential flow
cites work: Accelerated scalar dissipation in a vortex
cites work: Conformal mapping of some non-harmonic functions in transport theory
cites work: Reaction enhancement of isolated scalars by vortex stirring
cites work: VORTEX DYNAMICS IN TURBULENCE
description: scientific article; zbMATH DE number 6962660