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Taylor–Green vortex : ウィキペディア英語版
Taylor–Green vortex
In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates. It is named after the British physicist and mathematician Geoffrey Ingram Taylor and his collaborator A. E. Green.〔
Taylor, G. I. and Green, A. E., ''Mechanism of the Production of Small Eddies from Large Ones'', Proc. R. Soc. Lond. A, 158, 499–521 (1937).〕
==Original work==

In the original work of Taylor and Green,〔 a particular flow is analyzed in three spatial dimensions, with the three velocity components \mathbf=(u,v,w) at time t=0 specified by
:
u = A \cos ax \sin by \sin cz,

:
v = B \sin ax \cos by \sin cz,

:
w = C \sin ax \sin by \cos cz.

The continuity equation \nabla \cdot \mathbf=0 determines that Aa+Bb+Cc=0. The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step-by-step solution as time progresses.
An exact solution in two spatial dimensions is known, and is presented below.

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