期刊
INDIAN JOURNAL OF PHYSICS
卷 91, 期 9, 页码 1089-1094出版社
INDIAN ASSOC CULTIVATION SCIENCE
DOI: 10.1007/s12648-017-0999-x
关键词
Vortex; Navier-Stokes equations; Two-dimensional flow
资金
- RAMP
- D Center for reduction of Non-CO2 Greenhouse gases - Korea Ministry of Environment (MOE) as Global Top Environment RD Program [RE2015001690003]
A method to obtain a time-independent vortex solution of a nonlinear differential equation describing two-dimensional flow is investigated. In the usual way, starting from the Navier-Stokes equation the vortex equation is derived by taking a curl operation. After rearranging the equation of the vortex, we get a continuity equation or a divergence-free equation: partial derivative V-1(1) + partial derivative V-2(2) = 0. Additional irrotationality of V-1 and V-2 leads us to the Cauchy-Riemann condition satisfied by a newly introduced stream function Psi and velocity potential Phi. As a result, if we know V-1 and V-2 or a combination of two, the differential equation is mapped to a lower-order partial differential equation. This differential equation is the one satisfied by the stream function psi where the vorticity vector omega is given by -(partial derivative(2)(1)+partial derivative(2)(2))psi. A simple solution is discussed for the two different limits of viscosity.
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